Set Theory Quiz Questions And Answers

1.

The Venn Diagram shows a Disjoint set

True

False

The Venn Diagram shows a disjoint set because there are two separate circles that do not overlap or share any elements. In a disjoint set, the elements in one set are completely separate from the elements in the other set.

Explanation

The Venn Diagram shows a disjoint set because there are two separate circles that do not overlap or share any elements. In a disjoint set, the elements in one set are completely separate from the elements in the other set.

2. If A = {1, 5, 3, 7, 9} and B = {2, 3, 4, 5, 6}, what is A ∩ B?

{ 1,5,3,7,9}

{2,3,4,5,6}

{ 3, 5}

None of these

The intersection of two sets, denoted by ∩, includes only the elements that are common to both sets. Here, set A contains {1, 5, 3, 7, 9}, and set B contains {2, 3, 4, 5, 6}. The elements 3 and 5 are present in both sets. Therefore, the correct intersection is {3, 5}.

Explanation

The intersection of two sets, denoted by ∩, includes only the elements that are common to both sets. Here, set A contains {1, 5, 3, 7, 9}, and set B contains {2, 3, 4, 5, 6}. The elements 3 and 5 are present in both sets. Therefore, the correct intersection is {3, 5}.

3. P u B = { 2,2, 4, 6, 8, 18,15,3, 47}

True

False

The given statement is false because the set P u B contains multiple occurrences of the number 2, which violates the definition of a set. In a set, each element should be unique and not repeated. Therefore, the correct answer is false.

Explanation

The given statement is false because the set P u B contains multiple occurrences of the number 2, which violates the definition of a set. In a set, each element should be unique and not repeated. Therefore, the correct answer is false.

4. The intersection of two sets is the set of all members that are common to both sets.

True

False

The statement is true because the intersection of two sets is defined as the set that contains all the elements that are present in both sets. In other words, it is the set of common elements between the two sets. If there are no common elements, then the intersection would be an empty set.

Explanation

The statement is true because the intersection of two sets is defined as the set that contains all the elements that are present in both sets. In other words, it is the set of common elements between the two sets. If there are no common elements, then the intersection would be an empty set.

5. If A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6}, what does A ∪ B represent?

{3,4,6}

{2,4,6}

{1,10,90}

{1,2,3,4,5,6}

Explanation

6. The symbol U is used to indicate the intersection of sets.

True

False

The symbol "∪" represents the union of sets, which combines all elements from both sets. The correct symbol for the intersection of sets is "∩", which includes only the elements common to both sets. Thus, the given statement is false.

Explanation

The symbol "∪" represents the union of sets, which combines all elements from both sets. The correct symbol for the intersection of sets is "∩", which includes only the elements common to both sets. Thus, the given statement is false.

7. The ____ of sets is the set of all the members of both sets without repeating any of the members in the sets.

Union

Pair

Numbers

None of these

The union of sets is the set that contains all the elements from both sets without any repetition. It combines the elements of both sets into a single set, ensuring that no duplicate elements are included.

Explanation

The union of sets is the set that contains all the elements from both sets without any repetition. It combines the elements of both sets into a single set, ensuring that no duplicate elements are included.

8. Every set must have numbers.

True

False

This statement is incorrect. Every set does not have to have numbers. A set can contain any type of elements, including numbers, letters, or even objects. Therefore, the correct answer is False.

Explanation

This statement is incorrect. Every set does not have to have numbers. A set can contain any type of elements, including numbers, letters, or even objects. Therefore, the correct answer is False.

9. A disjoint set is

Two sets that have no members in common

The set of all the members in both sets without creating any of the members in the sets

The set of all members that are common to both sets

The set of all the members that are partially common

A disjoint set refers to two sets that have no members in common. This means that there is no element that is present in both sets. In other words, the intersection of the two sets is an empty set.

Explanation

A disjoint set refers to two sets that have no members in common. This means that there is no element that is present in both sets. In other words, the intersection of the two sets is an empty set.

10. A = {1,2,3} and B = {4,5,6} then A n B = ______?

{}

Prime numbers

Universal set

None of these

The symbol "n" represents the intersection of two sets, which means finding the common elements between them. In this case, set A and set B have no common elements, as they are completely distinct sets. Therefore, the intersection of A and B is an empty set, represented by {}. The answer "None of these" is incorrect because the correct answer is an empty set, not one of the other options provided.

Explanation

The symbol "n" represents the intersection of two sets, which means finding the common elements between them. In this case, set A and set B have no common elements, as they are completely distinct sets. Therefore, the intersection of A and B is an empty set, represented by {}. The answer "None of these" is incorrect because the correct answer is an empty set, not one of the other options provided.

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