This set of Discrete Mathematics Quiz focuses on “Cartesian Product of Sets”.

1. Let set A ={1, 2} and C be {3, 4} then A X B (Cartesian product of set A and B) is

a) {1, 2, 3, 4}

b) {(1, 3) ,(2, 4)}

c) {(1, 3) , (2, 4), (1, 4) , (2, 3) }

d) {(3, 1), (4, 1)}

View Answer

Explanation: In set A X B :{ (c , d) |c ∈ A and d ∈ B}.

2. If set A has 4 elements and B has 3 elements then set n(A X B) is

a) 12

b) 14

c) 24

d) 7

View Answer

Explanation: The total elements in n(A X B) = n(A) * n(B).

3. If set A has 3 elements then number of elements in A X A X A are

a) 9

b) 27

c) 6

d)19

View Answer

Explanation: n(A X A X A) = n(A)* n(A)* n(A).

4. Which of the following statements regarding sets is false ?

a) A X B = B X A

b) A X B ≠ B X A

c) n(A X B) = n(A) * n(B)

d) All of the mentioned

View Answer

Explanation: The Cartesian product of sets is not commutative.

5. If n(A X B) = n(B X A) = 36 then which of the following may hold true?

a) n(A)=2, n(B)=18

b) n(A)=9, n(B)=4

c) n(A)=6, n(b)=6

d) None of the mentioned

View Answer

Explanation: n(A) should be equal to n(B) for n(A X B) = n(B x A).

6. If C = {1} then C X (C X C) = (C X C) X C the given statement is

a) True

b) False

View Answer

Explanation: The Cartesian product is not associative, (C × C) × C = { ((1, 1), 1) } ≠ { (1,(1, 1)) } = C × (C × C).

7. Let the sets be A, B, C, D then (A ∩ B) X (C ∩ D) is equivalent to

a) (A X C) ∩ (B X D)

b) (A X D) U (B X C)

c) (A X C) U ( B X D)

d) None of the mentioned

View Answer

Explanation: (A ∩ B) X (C ∩ D) = (A X C) ∩ (B X D) but in case of unions this is not true.

8. If A ⊆ B then A X C ⊆ B X C the given statement is

a) True

b) False

View Answer

Explanation: Let an arbitrary element x ∈ A and y ∈ C, then x ∈ B (subset property), (x,y) ∈ AX C also (x,y) ∈ B X C. This implies A X C ⊆ B X C.

9. If set A and B have 3 and 4 elements respectively then the number of subsets of set (A X B) is

a) 1024

b) 2048

c) 512

d) 4096

View Answer

Explanation: The A X B has 12 elements ,then the number of subset are 2 12 = 4096.

10. If set A X B=B X A then which of the following sets may satisfy

a) A={1, 2, 3} , B={1, 2, 3, 4}

b) A={1, 2} , B={2, 1}

c) A={1, 2, 3} , B={2, 3, 4}

d) None of the mentioned

View Answer

Explanation: For set A X B = B X A ,this is possible only when set A = B.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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