Sets - Notation And Theory

1. Match the sets below with their corresponding descriptions.

A subset of the universal set

The Universal Set

Disjoint sets

A subset of A

A set that is included in A', the complement of A.

A set that is not disjoint with B

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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

True

False

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.

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.

3. For the sets below, match the descriptions with their corresponding answer.

n(E)

n(E')

n(U)

n(EUF)

n(E∩F)

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4. 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?

K = {All the letters in Karl's Name}

V = {A,E,I,O,U,Y}

O = {1,3,5,7,9}

Both A and B

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.

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.

5. 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.

True

False

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.

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.

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

Robin, Starling, Mallard, Duck-billed Platypus, Rabbit, Dog, Cat, Horse

Whale

Duck-bill Platypus

Both A and C

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.

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.

7. 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.

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.

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

True

False

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.

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.

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

Whale

Robin, Starling, Mallard

Duck-billed Platypus

Whale, Rabbit, Dog, Cat, Horse

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'.

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'.

10. 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)

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}.

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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11. 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)

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}.

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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