250+ TOP MCQs on Power Sets & Answers | Class 11 Maths

Mathematics Multiple Choice Questions on “Power Sets”.

1. Which of the following is not the element of power set of {2,3}?
a) Φ
b) {2}
c) {{2,3}}
d) {2,3}
Answer: c
Clarification: Power set of set A is set of all subsets of set A. Each element of power set is subset of the given set. Subsets of {2,3} is Φ, {2}, {3}, {2,3}.

2. If a set A has 3 elements then find the number of elements in power set of set A.
a) 1
b) 2
c) 8
d) 27
Answer: c
Clarification: Power set of set A is set of all subsets of set A. Set with m elements has 2^m subsets. So, number of elements in power set of set A is 2³=8.

3. If set A = {1,2,3} then which of the following is incorrect?
a) Φ∈A
b) Φ∈P(A)
c) Φ⊂A
d) Φ⊂P(A)
Answer: a
Clarification: Null set is subset of every set so, Φ⊂P(A) and Φ⊂A. Since Φ⊂A and power set of set A is set of all subsets of set A so, Φ∈P(A). Hence Φ∈A is incorrect.

4. If set X = {2,3,5,7}, then n[P(X)] is _____________
a) 8
b) 16
c) 32
d) 64
Answer: b
Clarification: Power set of set X is set of all subsets of set X. Set with m elements has 2^m subsets. So, number of elements in power set of set X is 2⁴=16.

5. How many elements are there in P(A), if A = φ?
a) 1
b) 2
c) 3
d) 4
Answer: a
Clarification: If A = φ then n(A)=0. Set with m elements has 2^m subsets. So, number of elements in P(A) is 20=1. P(A) = {φ}.

6. If A = {a, b, c} then P(A) = {{a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b, c}}.
a) True
b) False
Answer: b
Clarification: A= {a, b, c}. Possible subsets of set A are φ, {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b, c}. So, P(A) = {φ, {a}, {b}, {c}, {a, b}, {b, c}, {a, c}, {a, b, c}}.

7. If X = {1,2} then P(X) = {φ, {1}, {2}, {1,2}}.
a) True
b) False
Answer: a
Clarification: X= {1,2}. Possible subsets of set X are φ, {1}, {2}, {1,2}. Power set of set X is set of all subsets of set X. P(X)= {φ, {1}, {2}, {1,2}}.

8. Cardinality of the power set of {0, 1, 2 . . ., 6} is _________
a) 1024
b) 4096
c) 512
d) 2048
Answer: d
Clarification: Given set has 7 elements from 0 to 6. So, power set of the given set has 2⁷ i.e. 128 elements. Hence cardinality of the power set of {0, 1, 2 . . ., 6} is 128.

9. If a set A={x: x is a prime number less than 4} then n[P(P(A))] is ______________
a) 8
b) 16
c) 32
d) 64
Answer: b
Clarification: A={2,3}. Power set of A i.e. P(A) has 2²=4 elements. n[P(A)]=4. P(P(A)) has 2⁴=16 elements. n[P(P(A))] is 16.

10. If set A={Φ} then P(A) is ___________
a) {Φ}
b) {{Φ}}
c) {Φ, {Φ}}
d) Φ
Answer: c
Clarification: Set A={Φ} => Set A has one element Φ so, subsets of set A are Φ, {Φ}. So, P(A) = {{Φ, {Φ}}.