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

View Answer

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

View Answer

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) 4^{5}

c) 20

d) 5^{4}

View Answer

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.

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

View Answer

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

View Answer

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).

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

View Answer

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

View Answer

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}

View Answer

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}

View Answer

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

View Answer

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 2

^{r}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 2

^{6}i.e. 64.

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