Diskretna Matematika 1. Kolokvijum

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Diskretna Matematika 1. Kolokvijum - Quiz

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  • 2. 

    Recenica 2+2=3 je:

    • Iskaz

    • Iskaz koji je tacan

    • Iskaz koji nije tacan

    • Nije iskaz

    Correct Answer(s)
    A. Iskaz
    A. Iskaz koji nije tacan
    Explanation
    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.

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  • 3. 

    Čuvena misao Rene Dekarta glasi:

    • Mislim dakle postojim

    • Mislim dakle ne postojim

    • Cogito ergo sum

    • Ne mislim, a postojim

    Correct Answer(s)
    A. Mislim dakle postojim
    A. Cogito ergo sum
    Explanation
    The correct answer is "mislim dakle postojim, cogito ergo sum." This is because it is the correct translation of the famous quote by René Descartes, which means "I think, therefore I am." It is a fundamental philosophical statement that asserts the existence of oneself based on the act of thinking.

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  • 4. 

    Logika je nauka o?

    • Metodama pravilnog misljenja

    • Zakljucivanja

    • Algoritmima

    • Skupovima

    Correct Answer(s)
    A. Metodama pravilnog misljenja
    A. Zakljucivanja
    Explanation
    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.

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  • 5. 

    Tvorac logike je?

    • Aristotel

    • Arhimed

    • Euklid

    • Platon

    Correct Answer
    A. Aristotel
    Explanation
    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.

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  • 6. 

    Iskaz je recenica koja je:

    • Moze samo da bude tacna ili netacna

    • Uvek tacna

    • Uvek netacna

    • Ne znamo njenu tacnost

    Correct Answer
    A. Moze samo da bude tacna ili netacna
    Explanation
    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.

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  • 7. 

    Skup čine elementi koji:

    • Imaju samo jednu zajedničku osobinu

    • Imaju bar jednu zajedničku osobinu

    • Imaju tačno dve zajedničke osobine

    • Nemaju zajedničkih osobina

    Correct Answer
    A. Imaju bar jednu zajedničku osobinu
    Explanation
    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.

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  • 8. 

    Iskaz se jos naziva:

    • Sud

    • Tautologija

    • Kontrapozicija

    • Recenica

    Correct Answer
    A. Sud
    Explanation
    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.

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  • 9. 

    Prazan skup je skup koji:

    • Nema elemenata

    • čiji je element prazan skup

    • Ne postoji prazan skup

    • čiji je element nula

    Correct Answer
    A. Nema elemenata
    Explanation
    The correct answer is "nema elemenata." This means that an empty set is a set that does not have any elements.

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  • 10. 

    Po definiciji 0! je:

    • 1

    • 0

    • Nema resenja

    • Bilo koji broj

    Correct Answer
    A. 1
    Explanation
    The correct answer is 1. By definition, 0! (zero factorial) is equal to 1. This is a mathematical convention that is used to simplify calculations and maintain consistency in factorial calculations.

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  • 11. 

    Recenica 1+2=3 je:

    • Iskaz

    • Iskaz koji je tacan

    • Iskaz koji nije tacan

    • Nije iskaz

    Correct Answer(s)
    A. Iskaz
    A. Iskaz koji je tacan
    Explanation
    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.

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  • 12. 

    Skupovnu relaciju jednako definišemo pomoću logičke operacije :

    • Ekvivalencije

    • Konjukcije

    • Implikacije

    • Disjunkcije

    Correct Answer
    A. Ekvivalencije
    Explanation
    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.

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  • 13. 

    Sta je relacija:

    • Veza

    • Operacija

    • Odnos

    • Funkcija

    Correct Answer(s)
    A. Veza
    A. Odnos
    Explanation
    The correct answer is "veza, odnos". In the context of the question, "relacija" can be translated as "relation" in English. A relation is a connection or association between two or more things. It can be understood as a link or bond that exists between entities. Therefore, "veza" (meaning "connection" or "link") and "odnos" (meaning "relationship") accurately describe the concept of a relation. The other options, "operacija" (meaning "operation") and "funkcija" (meaning "function"), do not accurately capture the meaning of "relacija" in this context.

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  • 14. 

    Matematicka logika je uticala na razvoj

    • Digitalnih elektronskih racunara

    • Industrijske revolucije

    • Teorije grafova

    • Digitrona

    Correct Answer
    A. Digitalnih elektronskih racunara
    Explanation
    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.

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  • 15. 

    Recenica x+2=3 je:

    • Nije iskaz

    • Iskaz koji nije tacan

    • Iskaz koji je tacan

    • Iskaz

    Correct Answer
    A. Nije iskaz
    Explanation
    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.

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  • 16. 

    Koji od navedenih  zapisa predstavljaju dovoljan uslov za rečenicu x  je pozitivan broj.

    • X je vece od 1

    • X je manje od 1

    • X je vece od 2

    • X je manje od 0

    Correct Answer(s)
    A. X je vece od 1
    A. X je vece od 2
    Explanation
    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.

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  • 17. 

    Skupovnu relaciju podskup definišemo pomoću logičke operacije :

    • Implikacije

    • Ekvivalencije

    • Konjukcije

    • Disjunkcije

    Correct Answer
    A. Implikacije
    Explanation
    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.

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  • 18. 

    Ako je skup A podskup skupa B onda su:

    • Svi elementi skupa A istovremeno i elementi skupa B

    • Svi elementi skupa B istovremeno i elementi skupa A

    • Svi elementi skupova A i B su isti

    • Svi elementi skupa A i B su različiti

    Correct Answer
    A. Svi elementi skupa A istovremeno i elementi skupa B
    Explanation
    If set A is a subset of set B, it means that all elements of set A are also elements of set B. Therefore, the correct answer is "svi elementi skupa A istovremeno i elementi skupa B" which translates to "all elements of set A are simultaneously elements of set B".

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  • 19. 

    Kombinatorika se bavi raspoređivanjem elemenata u:

    • ​​​​​​konačnim skupovima

    • Beskonačnim skupovima

    • Nije bitan broj elementa skupa

    • Ne bavi se raspoređivanjem elemenata skupova

    Correct Answer
    A. ​​​​​​konačnim skupovima
    Explanation
    Kombinatorika se bavi raspoređivanjem elemenata u konačnim skupovima. To znači da se proučava način na koji se elementi mogu organizovati ili aranžirati unutar skupa koji ima konačan broj elemenata. Ova grana matematike se bavi brojanjem, kombinacijama i permutacijama elemenata u skupovima kako bi se izračunale različite mogućnosti raspoređivanja.

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  • 20. 

    Tautologije je formula koja je

    • Uvek tacna

    • Uvek netacna

    • Ponekad tacna

    • Ponekad netacna

    Correct Answer
    A. Uvek tacna
    Explanation
    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.

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  • 21. 

    Matematicka logika se intezivno razvija od:

    • Pocetka 19. veka

    • 4 veka pre nove ere

    • 17 veka

    • 7 veka

    Correct Answer
    A. Pocetka 19. veka
    Explanation
    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.

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  • 22. 

    Funkcija u odnosu na relaciju je:

    • širi pojam

    • Isti pojam

    • Uži pojam

    • Nemaju veze

    Correct Answer
    A. Uži pojam
    Explanation
    The given correct answer for this question is "uži pojam". This means that the function is a narrower concept compared to the relation. In other words, a function is a specific type of relation where each input has exactly one output, while a relation is a more general concept that can have multiple outputs for a single input. Therefore, the function is a subset or a narrower concept within the broader concept of relation.

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  • 23. 

    Kombinatorika se bavi odredjivanjem broja:

    • Različitih rasporeda elemenata nekog skupa

    • Istih rasporeda elemenata nekog skupa

    • Ne bavi se rasporedima elemenata nekog skupa

    • Verovatnoća slučajnih događaja

    Correct Answer
    A. Različitih rasporeda elemenata nekog skupa
    Explanation
    Kombinatorika se bavi određivanjem broja različitih rasporeda elemenata nekog skupa. Ova grana matematike proučava načine na koje se elementi mogu organizovati ili kombinovati na različite načine, bez obzira na redosled ili ponavljanje elemenata. Ova definicija se slaže sa odgovorom "različitih rasporeda elemenata nekog skupa".

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  • 24. 

    Različiti rasporedi u kombinatorici  su:

    • Permutacije

    • Varijacije

    • Kombinacije

    • Komutacije

    Correct Answer(s)
    A. Permutacije
    A. Varijacije
    A. Kombinacije
    Explanation
    The given answer lists different types of arrangements in combinatorics. Permutations refer to the arrangement of objects in a specific order, variations refer to the arrangement of objects where the order matters but some objects may be repeated, and combinations refer to the arrangement of objects where the order does not matter and no objects are repeated. However, "komutacije" is not a term commonly used in combinatorics, so it is likely a typo or an incorrect term.

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  • 25. 

    Koliko mogucnosti ima iskazna tablica koja ima 4 iskazna slova (redova)

    • 16

    • 2

    • 4

    • 8

    Correct Answer
    A. 16
    Explanation
    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.

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  • 26. 

    Realnih brojeva ima isto koliko i :

    • Prirodnih brojeva

    • Neparnih prirodnih brojeva

    • Celih brojeva

    • Tačaka na brojnoj pravoj

    Correct Answer
    A. Tačaka na brojnoj pravoj
    Explanation
    The number of real numbers is equal to the number of points on the number line. This is because every point on the number line represents a unique real number, and vice versa. Therefore, the number of real numbers is the same as the number of points on the number line.

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  • 27. 

    Relacija ekvivalencije je:

    • Jednako

    • Manje

    • Manje ili jednako

    • Podudarno

    Correct Answer(s)
    A. Jednako
    A. Podudarno
    Explanation
    The correct answer is "jednako, podudarno" because a relation of equivalence means that it satisfies three properties: reflexivity (every element is related to itself), symmetry (if a is related to b, then b is related to a), and transitivity (if a is related to b and b is related to c, then a is related to c). The terms "jednako" (equal) and "podudarno" (congruent) capture the idea of these properties, as two elements that are equal or congruent satisfy the properties of an equivalence relation.

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  • 28. 

    Injekcija je:

    • 1-1 preslikavanje

    • Na preslikavanje

    • 1-1 i na preslikavanje

    • Obostrano-jednoznačno preslikavanje

    Correct Answer
    A. 1-1 preslikavanje
    Explanation
    The correct answer is "1-1 preslikavanje." In mathematics, a 1-1 preslikavanje refers to a one-to-one mapping or injection. This means that each element in the domain is uniquely mapped to an element in the codomain, and no two elements in the domain are mapped to the same element in the codomain.

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  • 29. 

    Skup vrednosti nezavisno promenljive x za koje je definisana funkcija nazivamo:

    • Domen

    • Kodomen

    • Oblast definisanosti funkcije

    • Skup vrednosti funkcije

    Correct Answer(s)
    A. Domen
    A. Oblast definisanosti funkcije
    Explanation
    The correct answer is "domen, oblast definisanosti funkcije". The domain of a function refers to the set of all possible input values for the independent variable, while the range or "skup vrednosti funkcije" refers to the set of all possible output values. The "oblast definisanosti funkcije" refers to the set of all input values for which the function is defined or can be evaluated.

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  • 30. 

    Obrazac za izačunavanje permutacija mora se dokazatati:

    • Principom matematičke dedukcije

    • Principom matematičke indukcije

    • Metodom kontrapozicije

    • Metodom kontraprimera

    Correct Answer
    A. Principom matematičke indukcije
    Explanation
    The correct answer is "principom matematičke indukcije" because the calculation of permutations involves proving a statement for all possible values of a variable, typically using a base case and an inductive step. This method allows for a systematic and rigorous proof by considering the smallest possible case and then showing that if the statement holds for a particular value, it also holds for the next value. Therefore, the principle of mathematical induction is the appropriate method for proving the calculation of permutations.

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  • 31. 

    Osnovne logicke operacije su:

    • Unija i presek

    • Disjunkcija i konjukcija

    • Sabiranje i oduzimanje

    • Implikacija i ekvivalencija

    Correct Answer(s)
    A. Disjunkcija i konjukcija
    A. Implikacija i ekvivalencija
    Explanation
    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.

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  • 32. 

    Binarne logicke operacije su:

    • Negacija

    • Disjunkcija

    • Konjukcija

    • Ekvivalencija

    Correct Answer(s)
    A. Disjunkcija
    A. Konjukcija
    A. Ekvivalencija
    Explanation
    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.

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  • 33. 

    Unarne logičke operacije su:

    • Negacija

    • Disjunkcija

    • Konjukcija

    • Ekvivalencija

    Correct Answer
    A. Negacija
    Explanation
    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.

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  • 34. 

    Konjukcija je:

    • Tacna je kada su iskazna slova tacna

    • Uvek tacna

    • Uvek netacna

    • Netacna je kada iskazna slova imaju istu istinitosnu vrednost

    Correct Answer
    A. Tacna je kada su iskazna slova tacna
    Explanation
    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.

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  • 35. 

    Ekvivalencija je:

    • Tačna je kada iskazna slova imaju istu istinitosnu vrednost

    • Tačna je kada iskazna slova različitu istinitosnu vrednost

    • Uvek tačna

    • Uvek netačna

    Correct Answer
    A. Tačna je kada iskazna slova imaju istu istinitosnu vrednost
    Explanation
    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.

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  • 36. 

    Pitagorina teorema je oblika:

    • Ekvivalencije

    • Disjunkcije

    • Konjukcije

    • Implikacije

    Correct Answer
    A. Ekvivalencije
    Explanation
    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.

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  • 37. 

    Prioritet logičkih operacija je sledeći:

    • Najveći prioritet ima negacija

    • Negacija, pa disjunkcija ili konjukcija, pa implikacija ili ekvivalencija

    • Nema prioriteta

    • Negacija, pa implikacija ili ekvivalencija, pa disjunkcija ili konjukcija

    Correct Answer(s)
    A. Najveći prioritet ima negacija
    A. Negacija, pa disjunkcija ili konjukcija, pa implikacija ili ekvivalencija
    Explanation
    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.

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  • 38. 

    Za grafičko predstavljanje skupova koriste se:

    • Venovi dijagrami

    • Veneovi dijagrami

    • Ojlerovi dijagrami

    • Arhimedovi dijagrami

    Correct Answer
    A. Venovi dijagrami
    Explanation
    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.

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  • 39. 

    Funkcija je preslikavanje kod koga

    • Jednoj vrednosti promenljive x odgovara jedna vrednost promenljive y

    • Jednoj vrednosti promenljive x odgovara više vrednosti promenljive y

    • Jednoj vrednosti promenljive y odgovara jedna vrednost promenljive x

    • Jednoj vrednosti promenljive x ne odgovara nijedna vrednost promenljive y

    Correct Answer
    A. Jednoj vrednosti promenljive x odgovara jedna vrednost promenljive y
    Explanation
    The correct answer is "jednoj vrednosti promenljive x odgovara jedna vrednost promenljive y". This means that for each value of variable x, there is only one corresponding value of variable y. In other words, each input value has a unique output value in this function.

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  • 40. 

    Klase ekvivalencije predstavljaju razlaganje datog skupa na:

    • Disjunktne poskupove

    • Bilo kakve podskupove

    • Disjunktne nadskupove

    • Ne predstavljaju razlaganje

    Correct Answer
    A. Disjunktne poskupove
    Explanation
    Klase ekvivalencije predstavljaju razlaganje datog skupa na disjunktne poskupove. To znači da se skup deli na grupe elemenata koji su međusobno ekvivalentni, gde svaka grupa sadrži elemente koji su slični jedni drugima, ali se razlikuju od elemenata u drugim grupama. Ove grupe su disjunktne, što znači da se ne preklapaju i ne dele zajedničke elemente. Klase ekvivalencije su osnovni koncept u teoriji skupova i igraju važnu ulogu u mnogim matematičkim disciplinama.

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  • 41. 

    Osobina tranzitivnosti povezuje :

    • Dva elementa skupa

    • Tri elementa skupa

    • Element sa samim sobom

    • 4 elementa skupa

    Correct Answer
    A. Tri elementa skupa
    Explanation
    The property of transitivity connects three elements of a set. This means that if element A is related to element B, and element B is related to element C, then element A is also related to element C. Therefore, the correct answer is "tri elementa skupa" (three elements of a set).

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  • 42. 

    Koliko ima permutacija od elementa a,a,b,b

    • 4

    • 24

    • 6

    • 12

    Correct Answer
    A. 6
    Explanation
    The number of permutations of the elements a,a,b,b can be calculated using the formula for permutations with repetition. In this case, there are 4 elements in total, with 2 repetitions of the letter a and 2 repetitions of the letter b. The formula for permutations with repetition is n! / (n1! * n2! * ... * nk!), where n is the total number of elements and n1, n2, etc. are the repetitions of each element. Applying this formula, we get 4! / (2! * 2!) = 24 / (2 * 2) = 6. Therefore, there are 6 permutations of the given elements.

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  • 43. 

    Iskazna slova se obelezavaju:

    • Malim slovima abecede

    • Velikim slovima abecede

    • Grckim slovima

    • Specijalnim znacima

    Correct Answer
    A. Malim slovima abecede
    Explanation
    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.

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  • 44. 

    Relacije su:

    • Paralelno

    • Normalno

    • Sabiranje

    • Mnozenje

    Correct Answer(s)
    A. Paralelno
    A. Normalno
    Explanation
    The given answer states that the relationships are "parallel" and "normal." This suggests that the relationships being referred to in the question are related to geometric or mathematical concepts. "Parallel" typically refers to lines or objects that are equidistant and never intersect, while "normal" can mean perpendicular or at right angles. Therefore, the relationships being described in this context could be referring to the orientation or alignment of objects or lines in a geometric or mathematical context.

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  • 45. 

    Surjekcija je:

    • 1-1 preslikavanje

    • Na preslikavanje

    • 1-1 i na preslikavanje

    • Obostrano-jednoznačno preslikavanje

    Correct Answer
    A. Na preslikavanje
    Explanation
    The correct answer is "na preslikavanje." This means that the function is onto, or that every element in the range has a corresponding element in the domain. In other words, every element in the codomain is mapped to by at least one element in the domain.

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  • 46. 

    Grafici inverznih funkcija su:

    • Simetrični u odnosu na koordinatni početak

    • Simetrični u odnosu na x-osu

    • Simetrični u odnosu na y-osu

    • Simetrični u odnosu na simetralu 1 i 3 kvadranta

    Correct Answer
    A. Simetrični u odnosu na simetralu 1 i 3 kvadranta
    Explanation
    The inverse functions are symmetric with respect to the bisector of the first and third quadrants. This means that if a point (x, y) lies on the graph of the inverse function, then the point (-x, -y) also lies on the graph. In other words, if (x, y) is a solution to the inverse function, then (-x, -y) is also a solution. This symmetry is not present with respect to the x-axis, y-axis, or the origin.

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  • 47. 

    Relacija je u odnosu na funkciju:

    • širi pojam

    • Isti pojam

    • Uži pojam

    • Nemaju veze

    Correct Answer
    A. širi pojam
    Explanation
    The correct answer is "širi pojam" because the term "relacija" refers to a broader concept or category compared to the term "funkcija". In other words, a "relacija" can encompass multiple functions within it, while a "funkcija" is a specific type of relation with a defined set of rules and properties. Therefore, "širi pojam" accurately describes the relationship between the two terms.

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  • 48. 

    Aristotel je definisao pravila:

    • Deduktivnog zakljucivanja

    • Induktivnog zaključivanja

    • Zaključivanja putem kontrapozicije (reducio ad absurdum)

    • Zaključivanja putem kontraprimera

    Correct Answer
    A. Deduktivnog zakljucivanja
    Explanation
    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.

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  • 49. 

    Negacija recenice: Postoje prirodni brojevi koji su veci od 10.

    • Svi prirodni brojevi nisu veci od 10

    • Svi prirodni brojevi su veci od 10

    • Neki prirodni brojevi su manji od 10

    • Postoje prirodni brojevi koji su manji od 10

    Correct Answer
    A. Svi prirodni brojevi nisu veci od 10
    Explanation
    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".

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