# Mathematics Questions and Answers – Cartesian Product of Sets

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This set of Mathematics Multiple Choice Questions & Answers focuses on “Cartesian Product of Sets”.

1. If P X Q is an empty set then which of the following is a null set?
a) only P
b) only Q
c) either P or Q
d) both P and Q

Explanation: If either set P or set Q is a null set then P X Q is an empty set.
i.e. if P is Φ or Q is Φ then P X Q = Φ.

2. If (a, b) = (x, y) then___________
a) a=x
b) a=y
c) a=y and b=x
d) a=x and b=y

Explanation: Two ordered pairs are said to be equal if and only if their corresponding elements are equal i.e. a=x and b=y.

3. If set P has 4 elements and set Q has 5 elements then find the number of elements in P X Q.
a) 9
b) 45
c) 20
d) 54

Explanation: If set P has m elements and set Q has n elements then P X Q has m*n elements.
Here, m=4 and n=5 therefore P X Q has 4*5=20 elements.
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4. If (x+2, y-3) = (5,7) then find values of x and y.
a) x=3 and y=10
b) x=3 and y=4
c) x=7 and y=4
d) x=7 and y=10

Explanation: Two ordered pairs are said to be equal if and only if their corresponding elements are equal. x+2=5 => x=3
y-3=7 => y=10
Hence, x=3 and y=10.

5. Is (a, b) = (b, a)?
a) True
b) False

Explanation: Since (a, b) is an ordered pair i.e. order of first and second element matters and hence they can’t be interchanged. So, (a, b) ≠ (b, a).
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6. If P X Q has 10 elements then which is not possible?
a) n(P)=1 and n(Q)=10
b) n(P)=10 and n(Q)=1
c) n(P)=2 and n(Q)=5
d) n(P)=5 and n(Q)=4

Explanation: If set P has m elements and set Q has n elements then P X Q has m*n elements.
m*n=10 => if m=1 then n=10,
if m=2 then n=5,
if m=5 then n=2 and if m=10 then n=1.

7. If P = Q then P X Q = Q X P is true or not?
a) True
b) False

Explanation: Let P = (x, y) and Q = (a, b)
P X Q = {(x, a), (x, b), (y, a), (y, b)}
Q X P = {(a, x), (a, y), (b, x), (b, y)}
If P = Q i.e. x=a and y=b then P X Q = {(a, a), (a, b), (b, a), (b, b)}
Q X P = {(a, a), (a, b), (b, a), (b, b)}.
Hence P X Q = Q X P.

8. If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set A.
a) {1}
b) {1, 2}
c) {1, a}
d) {a, b, c}

Explanation: In each ordered pair of A X B, first element belongs to set A and second element belongs to set B.
1,2 ∈ A so, A = {1, 2}.

9. If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set B.
a) {1}
b) {1, 2}
c) {1, a}
d) {a, b, c}

Explanation: In each ordered pair of A X B, first element belongs to set A and second element belongs to set B.
a, b, c ∈ B so, B = {a, b, c}.

10. If set A has 2 elements and set B has 3 elements then how many subsets does A X B have?
a) 6
b) 8
c) 32
d) 64

Explanation: If set A has m elements and set B has n elements then A X B has m*n elements.
We know, a set has 2r subsets if it has r number of elements.
Here, A X B has 2*3 = 6 elements. So, number of subsets of A X B will be 26 i.e. 64.

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