Discrete Mathematics Quiz 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)}
Answer: c
Clarification: 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
Answer: a
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: c
Clarification: 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 true or false.
a) True
b) False
Answer: b
Clarification: 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
Answer: a
Clarification: (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 true or false.
a) True
b) False
Answer: a
Clarification: 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
Answer: d
Clarification: The A X B has 12 elements, then the number of the 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
Answer: b
Clarification: For set A X B = B X A, this is possible only when set A = B.