Diskretna Matematika 1. Kolokvijum
Questions and Answers
- 1.
Logika je nauka o?
- A.
Metodama pravilnog misljenja
- B.
Zakljucivanja
- C.
Algoritmima
- D.
Skupovima
Correct Answer(s)
A. Metodama pravilnog misljenja
B. ZakljucivanjaExplanation
Logika je nauka o metodama pravilnog mišljenja i zaključivanja. Ova disciplina proučava različite načine na koje možemo donositi ispravne zaključke na osnovu rasuđivanja i argumentacije. Metode pravilnog mišljenja nam pomažu da razumemo kako da koristimo logičke principe i pravila kako bismo došli do tačnih zaključaka. Zaključivanje je ključni deo logike, jer nam omogućava da izvodimo nove informacije ili tvrdnje iz već postojećih. Stoga, odgovor "metodama pravilnog mišljenja, zaključivanja" je tačan.Rate this question:
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- 2.
Tvorac logike je?
- A.
Aristotel
- B.
Arhimed
- C.
Euklid
- D.
Platon
Correct Answer
A. AristotelExplanation
Aristotel je tvorac logike jer je bio grčki filozof koji je prvi sistematski razvio logičko razmišljanje i postavio osnove formalne logike. Njegovo delo "Organon" smatra se temeljem zapadne logike i uticalo je na razvoj filozofije i nauke. Aristotel je razvio koncepte kao što su zaključivanje, premisa, syllogism i kategorije, koji su postali osnova za razumijevanje i analizu logičkih argumenata. Stoga, Aristotel se smatra tvorcem logike.Rate this question:
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- 3.
Aristotel je definisao pravila:
- A.
Deduktivnog zakljucivanja
- B.
Induktivnog zaključivanja
- C.
Zaključivanja putem kontrapozicije (reducio ad absurdum)
- D.
Zaključivanja putem kontraprimera
Correct Answer
A. Deduktivnog zakljucivanjaExplanation
Aristotel je definisao pravila deduktivnog zaključivanja. Deduktivno zaključivanje je proces izvođenja novih informacija iz postojećih činjenica i pretpostavki putem logičkih pravila. Aristotel je razvio sistem logike koji je uključivao syllogism, koji je bio osnova za deduktivno zaključivanje. Ova pravila omogućavaju da se iz općih pretpostavki izvedu specifični zaključci. Dakle, Aristotel je bio pionir u definiranju pravila deduktivnog zaključivanja.Rate this question:
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- 4.
Matematicka logika je uticala na razvoj
- A.
Digitalnih elektronskih racunara
- B.
Industrijske revolucije
- C.
Teorije grafova
- D.
Digitrona
Correct Answer
A. Digitalnih elektronskih racunaraExplanation
Matematicka logika je uticala na razvoj digitalnih elektronskih racunara. (Mathematical logic has influenced the development of digital electronic computers.) This answer correctly identifies the impact of mathematical logic on the development of digital electronic computers. Mathematical logic provided the foundation for the design and functioning of computers, enabling the creation of complex algorithms and logical operations.Rate this question:
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- 5.
Egzistencijalni kvantor se cita:
- A.
Svaki
- B.
Ma koji
- C.
Postoji
- D.
Neki
Correct Answer(s)
C. Postoji
D. NekiExplanation
The correct answer is "postoji, neki". This is because "postoji" means "there exists" in English, while "neki" means "some" or "a certain" in English. Therefore, when combined, "postoji, neki" can be translated as "there exists, some" or "there exists, a certain". This combination is commonly used to introduce the existential quantifier in logic and mathematics, indicating that there is at least one element that satisfies a given condition.Rate this question:
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- 6.
Univerzalni kvantor se cita:
- A.
Svaki
- B.
Ma koji
- C.
Bilo koji
- D.
Neki
Correct Answer(s)
A. Svaki
B. Ma koji
C. Bilo kojiExplanation
The correct answer for this question is "svaki, ma koji, bilo koji." These are all different ways to read the universal quantifier in Croatian, which is equivalent to the English word "every" or "any."Rate this question:
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- 7.
Negacija recenice: Svi prirodni brojevi su pozitivni.
- A.
Svi prirodni brojevi nisu pozitivni
- B.
Neki prirodni brojevi su pozitivni
- C.
Neki prirodni brojevi nisu pozitivni
- D.
Postoje prirodni brojevi koji nisu pozitivni
Correct Answer(s)
C. Neki prirodni brojevi nisu pozitivni
D. Postoje prirodni brojevi koji nisu pozitivniExplanation
The correct answer is "neki prirodni brojevi nisu pozitivni" and "postoje prirodni brojevi koji nisu pozitivni" because the original statement "Svi prirodni brojevi su pozitivni" is negated to mean "Not all natural numbers are positive." This implies that there are some natural numbers that are not positive, which is represented by the correct answers.Rate this question:
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- 8.
Negacija recenice: Postoje prirodni brojevi koji su veci od 10.
- A.
Svi prirodni brojevi nisu veci od 10
- B.
Svi prirodni brojevi su veci od 10
- C.
Neki prirodni brojevi su manji od 10
- D.
Postoje prirodni brojevi koji su manji od 10
Correct Answer
A. Svi prirodni brojevi nisu veci od 10Explanation
The given correct answer states that "svi prirodni brojevi nisu veci od 10" which translates to "not all natural numbers are greater than 10". This is the correct negation of the original statement "Postoje prirodni brojevi koji su veci od 10" which means "There exist natural numbers that are greater than 10".Rate this question:
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- 9.
Iskaz je recenica koja je:
- A.
Moze samo da bude tacna ili netacna
- B.
Uvek tacna
- C.
Uvek netacna
- D.
Ne znamo njenu tacnost
Correct Answer
A. Moze samo da bude tacna ili netacnaExplanation
The statement is asking about the nature of an "iskaz" (statement). The correct answer is that a statement can only be true or false, meaning it can only be either correct or incorrect. This suggests that there are no other possibilities for the truth value of a statement, and it cannot be partially true or partially false. Therefore, the statement is either true or false, and this is the only correct answer.Rate this question:
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- 10.
Iskaz se jos naziva:
- A.
Sud
- B.
Tautologija
- C.
Kontrapozicija
- D.
Recenica
Correct Answer
A. SudExplanation
The correct answer is "sud" because "sud" is the Serbian word for "statement" or "proposition." It refers to a declarative sentence that can be either true or false. The other options, "tautologija" (tautology), "kontrapozicija" (contraposition), and "recenica" (sentence), are not accurate translations of "statement" in this context.Rate this question:
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- 11.
Iskazna slova se obelezavaju:
- A.
Malim slovima abecede
- B.
Velikim slovima abecede
- C.
Grckim slovima
- D.
Specijalnim znacima
Correct Answer
A. Malim slovima abecedeExplanation
The correct answer is "malim slovima abecede." This means that lowercase letters of the alphabet are used to mark statements. This is a common convention in writing, where lowercase letters are used for regular text while uppercase letters are used for emphasis or headings.Rate this question:
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- 12.
Istinitosna vrednost iskaza je:
- A.
Tacno i netacno
- B.
1 i 0
- C.
True i false
- D.
1 i 2
Correct Answer(s)
A. Tacno i netacno
B. 1 i 0
C. True i falseExplanation
The correct answer is "tacno i netacno, 1 i 0, true i false." This is because in logic and programming, there are two possible boolean values: true and false, which can also be represented as 1 and 0. Therefore, the statement "tacno i netacno, 1 i 0, true i false" accurately represents the true values of an expression.Rate this question:
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- 13.
Recenica x+2=3 je:
- A.
Nije iskaz
- B.
Iskaz koji nije tacan
- C.
Iskaz koji je tacan
- D.
Iskaz
Correct Answer
A. Nije iskazExplanation
The given sentence "x+2=3" is not a proposition or statement because it contains a variable "x" which does not have a specific value assigned to it. Therefore, it cannot be evaluated as true or false. Hence, it is not a valid statement.Rate this question:
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- 14.
Recenica 1+2=3 je:
- A.
Iskaz
- B.
Iskaz koji je tacan
- C.
Iskaz koji nije tacan
- D.
Nije iskaz
Correct Answer(s)
A. Iskaz
B. Iskaz koji je tacanExplanation
The given correct answer for this question is "iskaz, iskaz koji je tacan". This means that the statement "1+2=3" is a proposition and it is a true proposition. In logic, a proposition is a statement that can be either true or false, and in this case, the statement "1+2=3" is true because the sum of 1 and 2 is indeed equal to 3.Rate this question:
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- 15.
Recenica 2+2=3 je:
- A.
Iskaz
- B.
Iskaz koji je tacan
- C.
Iskaz koji nije tacan
- D.
Nije iskaz
Correct Answer(s)
A. Iskaz
C. Iskaz koji nije tacanExplanation
The correct answer is "iskaz, iskaz koji nije tacan." This means that the sentence "2+2=3" is a statement, and it is a statement that is not true. In other words, it is a false statement.Rate this question:
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- 16.
Osnovne logicke operacije su:
- A.
Unija i presek
- B.
Disjunkcija i konjukcija
- C.
Sabiranje i oduzimanje
- D.
Implikacija i ekvivalencija
Correct Answer(s)
B. Disjunkcija i konjukcija
D. Implikacija i ekvivalencijaExplanation
The correct answer is "disjunkcija i konjukcija, implikacija i ekvivalencija." The explanation is that the basic logical operations are union and intersection, which are used in set theory. However, in propositional logic, the basic logical operations are disjunction (also known as "or") and conjunction (also known as "and"), which are used to combine propositions. Additionally, implication and equivalence are also basic logical operations in propositional logic, where implication represents "if...then" statements and equivalence represents "if and only if" statements.Rate this question:
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- 17.
Binarne logicke operacije su:
- A.
Negacija
- B.
Disjunkcija
- C.
Konjukcija
- D.
Ekvivalencija
Correct Answer(s)
B. Disjunkcija
C. Konjukcija
D. EkvivalencijaExplanation
The correct answer is "disjunkcija, konjukcija, ekvivalencija." In English, this translates to "disjunction, conjunction, equivalence." These are the three basic binary logical operations. Disjunction represents the logical OR operation, where at least one of the operands must be true for the result to be true. Conjunction represents the logical AND operation, where both operands must be true for the result to be true. Equivalence represents the logical equivalence operation, where the two operands have the same truth value.Rate this question:
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- 18.
Unarne logičke operacije su:
- A.
Negacija
- B.
Disjunkcija
- C.
Konjukcija
- D.
Ekvivalencija
Correct Answer
A. NegacijaExplanation
The correct answer is "negacija" because negacija is a unary logical operation that represents the opposite or negation of a proposition. It takes a single input and produces the opposite truth value as the input.Rate this question:
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- 19.
Konjukcija je:
- A.
Tacna je kada su iskazna slova tacna
- B.
Uvek tacna
- C.
Uvek netacna
- D.
Netacna je kada iskazna slova imaju istu istinitosnu vrednost
Correct Answer
A. Tacna je kada su iskazna slova tacnaExplanation
The correct answer is "tacna je kada su iskazna slova tacna." This means that a conjunction is true only when both of the propositional letters (or variables) are true. In other words, for a conjunction to be true, both statements connected by the conjunction must be true. If either or both of the statements are false, then the conjunction is false.Rate this question:
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- 20.
Ekvivalencija je:
- A.
Tačna je kada iskazna slova imaju istu istinitosnu vrednost
- B.
Tačna je kada iskazna slova različitu istinitosnu vrednost
- C.
Uvek tačna
- D.
Uvek netačna
Correct Answer
A. Tačna je kada iskazna slova imaju istu istinitosnu vrednostExplanation
The correct answer is "tačna je kada iskazna slova imaju istu istinitosnu vrednost." This means that equivalence is true when the propositional letters have the same truth value.Rate this question:
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- 21.
Implikacija p --> q se moze procitati i kao:
- A.
Q je potreban uslov za p
- B.
P je dovoljan uslov za q
- C.
P je potreban uslov za q
- D.
Q je dovoljan uslov za p
Correct Answer(s)
A. Q je potreban uslov za p
B. P je dovoljan uslov za qExplanation
The correct answer is "q je potreban uslov za p,p je dovoljan uslov za q". This answer correctly states that q is a necessary condition for p, meaning that if q is not true, then p cannot be true. Additionally, it states that p is a sufficient condition for q, meaning that if p is true, then q must also be true.Rate this question:
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- 22.
Ekvivalencija p <=> q se moze procitati i kao
- A.
P je potreban i dovoljan uslov za q
- B.
P je potreban uslov za q
- C.
P ako q
- D.
P akko q
Correct Answer(s)
A. P je potreban i dovoljan uslov za q
D. P akko qExplanation
The correct answer is "p je potreban i dovoljan uslov za q" and "p akko q". These statements indicate that p is both necessary and sufficient for q. In other words, if p is true, then q must also be true, and if q is true, then p must also be true. This shows a bidirectional relationship between p and q, where they depend on each other for their truth values.Rate this question:
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- 23.
Implikacija p => q se moze procitati i kao
- A.
Ako p onda q
- B.
Iz p sledi q
- C.
Iz q sledi p
- D.
P je pretpostavka posledice q
Correct Answer(s)
A. Ako p onda q
B. Iz p sledi q
D. P je pretpostavka posledice qExplanation
The correct answer is "Ako p onda q, Iz p sledi q, p je pretpostavka posledice q." This is because the given statement "Implikacija p => q se moze procitati i kao" is translated to "Implication p => q can be read as." The options provided in the answer are different ways to interpret or read the implication statement, and they all convey the same meaning.Rate this question:
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- 24.
Pitagorina teorema je oblika:
- A.
Ekvivalencije
- B.
Disjunkcije
- C.
Konjukcije
- D.
Implikacije
Correct Answer
A. EkvivalencijeExplanation
The correct answer is "Ekvivalencije" because the question is asking for the form of the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, the Pythagorean theorem can be expressed as an equivalence statement, where the two sides of the equation are equivalent to each other.Rate this question:
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- 25.
Recenica, 'Ako su prave paralelne, onda one nemaju zajednicke tacke', moze se procitati i :
- A.
Prave su paralelne, samo ako nemaju zajednicke tacke
- B.
Paralelnost pravih je dovaljan uslov za nepostojanje zajednickih tacaka
- C.
Paralelnost pravih je potreban uslov za nepostojanje zajednickih tacaka
- D.
Nepostojanje zajednickih tacaka je potreban uslov za paralelnost pravih
Correct Answer(s)
A. Prave su paralelne, samo ako nemaju zajednicke tacke
B. Paralelnost pravih je dovaljan uslov za nepostojanje zajednickih tacaka
D. Nepostojanje zajednickih tacaka je potreban uslov za paralelnost pravihExplanation
The correct answer is "prave su paralelne, samo ako nemaju zajednicke tacke". This statement accurately represents the given sentence, which states that if lines are parallel, they do not have any common points. The other options do not accurately represent the given sentence.Rate this question:
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- 26.
Koja od reci treba da stoji umesto tackica u recenici x>6 ..... x>3, tako da recenica bude tacna
- A.
Dovoljan
- B.
Potreban
- C.
Potreban i dovoljan
- D.
Povlaci
Correct Answer(s)
A. Dovoljan
D. PovlaciExplanation
The correct answer is "Dovoljan, Povlaci." In the given sentence "x > 6 .... x > 3," the missing word should be able to complete the sentence correctly. The word "Dovoljan" means "sufficient" in English, and it fits the context of the sentence because if x is greater than 6, it is sufficient to imply that x is also greater than 3. Additionally, the word "Povlaci" means "implies" in English, and it accurately describes the logical relationship between the two inequalities. Therefore, both "Dovoljan" and "Povlaci" are needed to make the sentence true.Rate this question:
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- 27.
Koja od reci treba da stoji umesto tackica u recenici, " X pripada skupu N .... X pripada skupu Z", tako da recenica bude tacna
- A.
Dovoljan
- B.
Potreban
- C.
Potreban i dovoljan
- D.
Povlaci
Correct Answer(s)
A. Dovoljan
D. PovlaciExplanation
The correct answer is "Dovoljan, Povlaci". The word "dovoljan" means "sufficient" in English, and "povlaci" means "implies". Therefore, the sentence can be translated as "X belongs to set N sufficient implies X belongs to set Z". This means that if X belongs to set N, it is sufficient to conclude that X belongs to set Z.Rate this question:
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- 28.
'Trougao je jednakokrak i nije jednakostraničan'. Koja od narednih rečenica je njen potreban i dovoljan uslov:
- A.
Dve stranice su jednake
- B.
Trougao ima tacno jednu osu simetrije
- C.
Uglovi su jednaki
- D.
Jedan ugao je prav
Correct Answer(s)
A. Dve stranice su jednake
B. Trougao ima tacno jednu osu simetrijeExplanation
For a triangle to be isosceles and not equilateral, it must have two equal sides. Additionally, an isosceles triangle must have exactly one axis of symmetry. The other options, such as equal angles or one right angle, are not necessary and sufficient conditions for an isosceles triangle.Rate this question:
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- 29.
Koji od navedenih zapisa predstavljaju dovoljan uslov za rečenicu x je pozitivan broj.
- A.
X je vece od 1
- B.
X je manje od 1
- C.
X je vece od 2
- D.
X je manje od 0
Correct Answer(s)
A. X je vece od 1
C. X je vece od 2Explanation
The correct answer is "x je vece od 1" and "x je vece od 2" because both statements indicate that x is greater than a positive number, which satisfies the condition of x being a positive number.Rate this question:
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- 30.
Koja od navedenih apisa predstavljaju dovoljan uslov za recenicu: x je broj deljiv 10.
- A.
Poslednja cifra je 0
- B.
X deljivo sa 20
- C.
X je deljivo sa 2
- D.
X je deljivo sa 5
Correct Answer(s)
A. Poslednja cifra je 0
B. X deljivo sa 20Explanation
The given answer states that for the sentence "x is a number divisible by 10" to be true, two conditions must be satisfied. First, the last digit of x must be 0, and second, x must be divisible by 20. This answer is correct because if the last digit of a number is 0, it means that the number is divisible by 10. Additionally, if a number is divisible by 20, it is also divisible by 10. Therefore, both conditions together are sufficient to conclude that x is a number divisible by 10.Rate this question:
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- 31.
Konverzacija recenice: Ako znam, onda cu poloziti test. glasi:
- A.
Ako polozim test, onda znam
- B.
Ako ne znam, onda necu poloziti test
- C.
Ako ne polozim test, onda ne znam
- D.
Polozicu test akko znam
Correct Answer
A. Ako polozim test, onda znamExplanation
The given answer states that "if I pass the test, then I know." This is a valid conclusion based on the given conversation. In the conversation, it is stated that "if I know, then I will pass the test" and "if I don't know, then I will not pass the test." Therefore, if someone does pass the test, it can be inferred that they must know the material.Rate this question:
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- 32.
Inverzija recenice: Ako znam, onda cu poloziti test, glasi:
- A.
Ako ne znam, onda necu poloziti test
- B.
Ako polozim test, onda znam
- C.
Ako ne polozim test, onda ne znam
- D.
Polozicu test akko znam
Correct Answer
A. Ako ne znam, onda necu poloziti testExplanation
The correct answer is "ako ne znam, onda necu poloziti test" because it accurately represents the inversion of the given sentence. The original sentence states that "if I know, then I will pass the test," and the correct answer reflects the inversion by stating "if I don't know, then I won't pass the test." This inversion maintains the logical relationship between knowing and passing the test.Rate this question:
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- 33.
Kontrapozicija rečenice: Ako znam, onda ću položiti test.glasi:
- A.
Ako ne polozim test, onda ne znam
- B.
Ako polozim test, onda znam
- C.
Ako ne znam, onda necu poloziti test
- D.
Polozicu test akko znam
Correct Answer
A. Ako ne polozim test, onda ne znamExplanation
The given answer states that if the person does not pass the test, then they do not know the material. This is the contrapositive of the original statement. According to the original statement, if the person knows the material, then they will pass the test. Therefore, if they do not pass the test, it implies that they do not know the material.Rate this question:
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- 34.
Tautologije je formula koja je
- A.
Uvek tacna
- B.
Uvek netacna
- C.
Ponekad tacna
- D.
Ponekad netacna
Correct Answer
A. Uvek tacnaExplanation
A tautology is a formula that is always true. This means that regardless of the truth values assigned to its variables, the formula will always evaluate to true. Therefore, the correct answer is "uvek tacna" which translates to "always true" in English.Rate this question:
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- 35.
Primeniti de Morganov zakon na sledeću rečenicu: 2 ili 3 je delilac broja 6
- A.
2>0 i 3 je delilac broja 6
- B.
2
- C.
2
- D.
2
Correct Answer
A. 2>0 i 3 je delilac broja 6 -
- 36.
Koliko mogucnosti ima iskazna tablica koja ima 4 iskazna slova (redova)
- A.
16
- B.
2
- C.
4
- D.
8
Correct Answer
A. 16Explanation
The question asks for the number of possibilities for a truth table with 4 propositional letters. In a truth table, each propositional letter can take on two possible truth values (true or false), and since there are 4 propositional letters, there are 2^4 = 16 possible combinations of truth values. Therefore, the correct answer is 16.Rate this question:
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- 37.
Iskaznu formulu cine:
- A.
Iskazna slova i znaci logičkih operacija
- B.
Samo 2 iskazna slova i znaci logičkih operacija
- C.
Iskazna slova i znaci skupovnih operacija
- D.
Iskazna slova, znaci logičkih operacija i obavezno zagrade
Correct Answer
A. Iskazna slova i znaci logičkih operacijaExplanation
The correct answer is "iskazna slova i znaci logičkih operacija" which translates to "propositional variables and logical operators" in English. This answer suggests that in the given context, the formula consists of propositional variables (also known as atomic propositions or basic statements) and logical operators (such as conjunction, disjunction, implication, etc.) which are used to form compound propositions. The other options mentioned in the question (only 2 propositional variables and logical operators, propositional variables and set operations, and propositional variables, logical operators, and parentheses) do not accurately describe the components of the formula.Rate this question:
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- 38.
Prioritet logičkih operacija je sledeći:
- A.
Najveći prioritet ima negacija
- B.
Negacija, pa disjunkcija ili konjukcija, pa implikacija ili ekvivalencija
- C.
Nema prioriteta
- D.
Negacija, pa implikacija ili ekvivalencija, pa disjunkcija ili konjukcija
Correct Answer(s)
A. Najveći prioritet ima negacija
B. Negacija, pa disjunkcija ili konjukcija, pa implikacija ili ekvivalencijaExplanation
The given answer states that the highest priority is given to negation, followed by either disjunction or conjunction, and then implication or equivalence. This means that when evaluating logical operations, negation should be performed first, followed by either disjunction or conjunction, and finally implication or equivalence.Rate this question:
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- 39.
Tautologije predstavljaju:
- A.
Zakone
- B.
Tacna tvrdjenja za bilo koji unos podataka
- C.
Pretpostavke
- D.
Proizvoljna tvrdjenja
Correct Answer(s)
A. Zakone
B. Tacna tvrdjenja za bilo koji unos podatakaExplanation
Tautologije su tvrdnje koje su uvijek istinite, neovisno o unesenim podacima. One se mogu smatrati zakonima jer predstavljaju opća pravila koja vrijede bez obzira na kontekst. Također, mogu se smatrati točnim tvrdnjama za bilo koji unos podataka jer će uvijek biti istinite, bez obzira na vrijednost podataka.Rate this question:
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- 40.
- Predikatske formule se grade pomoću :
- A.
Konstanti
- B.
Promenljivih
- C.
Kvantora
- D.
Nemogu da sadrže relacijske znake
Correct Answer(s)
A. Konstanti
B. Promenljivih
C. KvantoraExplanation
Predikatske formule se grade pomoću konstanti, promenljivih i kvantora. Konstante su određene vrednosti koje se koriste u formulama, promenljive su simboli koji predstavljaju objekte ili vrednosti koje mogu biti različite u različitim instancama formule, dok su kvantori simboli koji se koriste za opisivanje količine elemenata koji zadovoljavaju određeni uslov u formuli. Relacijski znaci, s druge strane, nisu dozvoljeni u predikatskim formulama.Rate this question:
- 41.
Matematicka logika se intezivno razvija od:
- A.
Pocetka 19. veka
- B.
4 veka pre nove ere
- C.
17 veka
- D.
7 veka
Correct Answer
A. Pocetka 19. vekaExplanation
Mathematical logic began to develop intensively in the early 19th century. This period marked significant advancements in the field, with the work of mathematicians such as George Boole and Augustus De Morgan laying the foundations for modern logic. The other options mentioned (4 centuries BC, 17th century, and 7th century) are not accurate in terms of the timeline of the development of mathematical logic.Rate this question:
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- 42.
Matematička logika je:
- A.
Nije primena logike matematici
- B.
Matematička disciplina koja je uvela strogost u definisanje pojmova
- C.
Primena logike u matematici
- D.
Deo filozofije
Correct Answer(s)
A. Nije primena logike matematici
B. Matematička disciplina koja je uvela strogost u definisanje pojmovaExplanation
Matematička logika je matematička disciplina koja je uvela strogost u definisanje pojmova. Ova disciplina se bavi proučavanjem matematičkih sistema, dok se primena logike u matematici odnosi na korišćenje logičkih principa i zakona u matematičkim dokazima. Matematička logika se takođe može smatrati delom filozofije, ali to nije jedino ispravno objašnjenje za ovaj pojam.Rate this question:
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- 43.
Skup čine elementi koji:
- A.
Imaju samo jednu zajedničku osobinu
- B.
Imaju bar jednu zajedničku osobinu
- C.
Imaju tačno dve zajedničke osobine
- D.
Nemaju zajedničkih osobina
Correct Answer
B. Imaju bar jednu zajedničku osobinuExplanation
The correct answer is "imaju bar jednu zajedničku osobinu" which means "have at least one common characteristic" in English. This implies that the elements in the set may have more than one common characteristic, but they must have at least one in common.Rate this question:
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- 44.
Partitivni skup je:
- A.
Skup svih podskupova datog skupa
- B.
Skup svih nadskupova datog skupa
- C.
Bilo koji podskup datog skupa
- D.
Proizvod dva skupa
Correct Answer
A. Skup svih podskupova datog skupaExplanation
A partitive set refers to the set that contains all the subsets of a given set. In other words, it is the set that consists of all possible combinations of elements from the original set, including the empty set and the original set itself. This definition aligns with the option "skup svih podskupova datog skupa" which translates to "set of all subsets of the given set" in English.Rate this question:
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- 45.
Za grafičko predstavljanje skupova koriste se:
- A.
Venovi dijagrami
- B.
Veneovi dijagrami
- C.
Ojlerovi dijagrami
- D.
Arhimedovi dijagrami
Correct Answer
A. Venovi dijagramiExplanation
Venovi dijagrami su grafikoni koji se koriste za vizualno prikazivanje skupova i njihovih odnosa. Ovi dijagrami se sastoje od preklapajućih krugova koji predstavljaju skupove, a presečni delovi krugova predstavljaju presek između skupova. Ovaj način predstavljanja skupova omogućava jasno i intuitivno razumevanje njihovih odnosa i preseka. Stoga, venovi dijagrami su odgovor na pitanje.Rate this question:
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- 46.
Disjunktni skupovi su oni:
- A.
čiji je presek prazan skup
- B.
Cija je unija prazan skup
- C.
čija je razlika prazan skup
- D.
čija je simetrična razlika prazan skup
Correct Answer
A. čiji je presek prazan skupExplanation
The correct answer is "čiji je presek prazan skup" which translates to "whose intersection is an empty set." This means that the elements in the two sets being compared have no common elements, resulting in an empty set when their intersection is taken.Rate this question:
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- 47.
Skupovnu operaciju uniju definišemo pomoću logičke operacije :
- A.
Disjunkcije
- B.
Ekvivalencije
- C.
Implikacije
- D.
Konjukcije
Correct Answer
A. DisjunkcijeExplanation
The correct answer is "disjunkcije". The union operation is defined using the logical operation of disjunction, which combines two sets and returns a new set that contains all the elements from both sets.Rate this question:
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- 48.
Skupovnu operaciju presek definišemo pomoću logičke operacije :
- A.
Konjukcije
- B.
Implikacije
- C.
Ekvivalencije
- D.
Disjunkcije
Correct Answer
A. KonjukcijeExplanation
The correct answer is "konjukcije" (conjunction). This means that the operation of intersection is defined using the logical operation of conjunction. Conjunction is a logical operation that returns true only if both of its operands are true. In the context of set operations, the intersection of two sets is the set that contains all the elements that are common to both sets. Therefore, the intersection operation can be defined using the logical operation of conjunction, where the two sets are the operands and the resulting set contains the common elements.Rate this question:
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- 49.
Skupovnu relaciju podskup definišemo pomoću logičke operacije :
- A.
Implikacije
- B.
Ekvivalencije
- C.
Konjukcije
- D.
Disjunkcije
Correct Answer
A. ImplikacijeExplanation
The correct answer is "implikacije." A relation can be defined as a subset of a Cartesian product of two sets. In the case of the implication operation, the relation is defined based on the truth values of two propositions. If the antecedent proposition is true, then the consequent proposition must also be true for the relation to hold. If the antecedent is false, the relation is considered true regardless of the truth value of the consequent. Therefore, the implication operation is used to define the subset relation in this context.Rate this question:
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- 50.
Skupovnu relaciju jednako definišemo pomoću logičke operacije :
- A.
Ekvivalencije
- B.
Konjukcije
- C.
Implikacije
- D.
Disjunkcije
Correct Answer
A. EkvivalencijeExplanation
The correct answer is "ekvivalencije" because the question is asking for the logical operation that defines the relation "Skupovna relacija jednako" (set equality relation). The relation of set equality is defined using the logical operation of equivalence, where two sets are considered equal if and only if they have exactly the same elements.Rate this question:
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