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}

View Answer

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

View Answer

Explanation: 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 2

^{3}=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)

View Answer

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.

4. If set X = {2,3,5,7}, then n[P(X)] is _____________

a) 8

b) 16

c) 32

d) 64

View Answer

Explanation: 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 2

^{4}=16.

5. How many elements are there in P(A), if A = φ?

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: 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

View Answer

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

View Answer

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

View Answer

Explanation: Given set has 7 elements from 0 to 6. So, power set of the given set has 2

^{7}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

View Answer

Explanation: A={2,3}. Power set of A i.e. P(A) has 2

^{2}=4 elements. n[P(A)]=4. P(P(A)) has 2

^{4}=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

View Answer

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

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