# Mathematics Questions and Answers – Power Sets

«
»

This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses 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}

Explanation: 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

Explanation: Power set of set A is set of all subsets of set A. Set with m elements has 2m 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)

Explanation: 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.
Note: Join free Sanfoundry classes at Telegram or Youtube

4. If set X = {2,3,5,7}, then n[P(X)] is _____________
a) 8
b) 16
c) 32
d) 64

Explanation: Power set of set X is set of all subsets of set X. Set with m elements has 2m 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

Explanation: If A = φ then n(A)=0. Set with m elements has 2m subsets. So, number of elements in P(A) is 20=1. P(A) = {φ}.
Take Mathematics - Class 11 Practice Tests - Chapterwise!
Start the Test Now: Chapter 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

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

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: 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

Explanation: Set A={Φ} => Set A has one element Φ so, subsets of set A are Φ, {Φ}. So, P(A) = {{Φ, {Φ}}.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

To practice all areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers. 