Sets - Notation And Theory

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| By Kkleinsasser

Kkleinsasser

Community Contributor

Quizzes Created: 5 | Total Attempts: 4,000

Questions: 11 | Attempts: 478 | Updated: Mar 21, 2023

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Questions and Answers

1.

Consider this universal set. A = {0,1,2,3,4,5,6,7,8,9} Which of the following sets is a subset of set A?
- A.
  
  K = {All the letters in Karl's Name}
- B.
  
  V = {A,E,I,O,U,Y}
- C.
  
  O = {1,3,5,7,9}
- D.
  
  Both A and B
Correct Answer
C. O = {1,3,5,7,9}

Explanation
The set O = {1,3,5,7,9} is a subset of set A = {0,1,2,3,4,5,6,7,8,9} because all the elements in set O are also present in set A. In other words, set O is completely contained within set A.

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2.

If set B is a subset of set A, then all the elements of set B are included in set A
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
If set B is a subset of set A, it means that all the elements in set B are also present in set A. In other words, set B is completely contained within set A. Therefore, the statement "all the elements of set B are included in set A" is true.

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3.

If set B is a subset of set A, than all the elements of set B are included in set A, and all the elements of set A are included in set B.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
If set B is a subset of set A, it means that all the elements of set B are included in set A. However, it does not necessarily mean that all the elements of set A are included in set B. Therefore, the statement that all the elements of set A are included in set B is false.

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4.

If A is a set, then A' is the ________________ of set A, and includes all the elements of the universal set that are not included in set A.

Correct Answer
complement

Explanation
The term "complement" refers to the set of all elements in the universal set that are not included in set A. In other words, it is the set that contains everything outside of set A.

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4
5.

Consider this universal set. D = {1,2,3,4,5,6,7,8,9,10,11,12,13,14} where O is a subset of D and O={odd numbers} List the subset O. (USE CORRECT NOTATION AND DO NOT USE SPACES IN YOUR ANSWER)

Correct Answer
O={1,3,5,7,9,11,13}

Explanation
The subset O is defined as the set of odd numbers from the universal set D. Therefore, O={1,3,5,7,9,11,13}.

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4
6.

Consider this universal set. D = {1,2,3,4,5,6,7,8,9,10,11,12,13,14} where O is a subset of D and O={odd numbers} List O'. (USE CORRECT NOTATION AND DO NOT USE SPACES IN YOUR ANSWER)

Correct Answer
O'={2,4,6,8,10,12,14}

Explanation
The set O' represents the complement of the set O, which consists of all the even numbers in the universal set D. In this case, since the universal set D contains all the numbers from 1 to 14, the even numbers in that range are 2, 4, 6, 8, 10, 12, and 14. Therefore, O'={2,4,6,8,10,12,14}.

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4
7.

For the sets below, EUF = {Duck-bill Platypus}
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The given answer is false because the set EUF is defined as {Duck-bill Platypus}. Therefore, the statement "EUF = {Duck-bill Platypus}" is true, not false.

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8.

For the sets below, what is included in E∩F?
- A.
  
  Robin, Starling, Mallard, Duck-billed Platypus, Rabbit, Dog, Cat, Horse
- B.
  
  Whale
- C.
  
  Duck-bill Platypus
- D.
  
  Both A and C
Correct Answer
C. Duck-bill Platypus

Explanation
The set E∩F represents the intersection of sets E and F, which means it includes all the elements that are common to both sets. In this case, the sets E and F are not explicitly given, but it can be inferred that E includes the elements Robin, Starling, Mallard, Duck-billed Platypus, Rabbit, Dog, Cat, and Horse, while F includes Duck-bill Platypus. Therefore, the only element that is common to both sets E and F is Duck-bill Platypus, which is included in E∩F.

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9.

For the Sets shown below, which creatures would be included in E'.
- A.
  
  Whale
- B.
  
  Robin, Starling, Mallard
- C.
  
  Duck-billed Platypus
- D.
  
  Whale, Rabbit, Dog, Cat, Horse
Correct Answer
D. Whale, Rabbit, Dog, Cat, Horse

Explanation
The set E' includes all the creatures that are present in the last set mentioned, which is "Whale, Rabbit, Dog, Cat, Horse". Therefore, the creatures Whale, Rabbit, Dog, Cat, and Horse would be included in E'.

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1
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Sets - Notation And Theory

Consider this universal set. A = {0,1,2,3,4,5,6,7,8,9} Which of the following sets is a subset of set A?

If set B is a subset of set A, then all the elements of set B are included in set A

If set B is a subset of set A, than all the elements of set B are included in set A, and all the elements of set A are included in set B.

If A is a set, then A' is the ________________ of set A, and includes all the elements of the universal set that are not included in set A.

Consider this universal set. D = {1,2,3,4,5,6,7,8,9,10,11,12,13,14} where O is a subset of D and O={odd numbers} List the subset O. (USE CORRECT NOTATION AND DO NOT USE SPACES IN YOUR ANSWER)

Consider this universal set. D = {1,2,3,4,5,6,7,8,9,10,11,12,13,14} where O is a subset of D and O={odd numbers} List O'. (USE CORRECT NOTATION AND DO NOT USE SPACES IN YOUR ANSWER)

For the sets below, EUF = {Duck-bill Platypus}

For the sets below, what is included in E∩F?

For the Sets shown below, which creatures would be included in E'.