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}
View Answer

Answer: c
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}.
advertisement

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

Answer: c
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)
View Answer

Answer: 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.
advertisement
advertisement

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

Answer: b
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
View Answer

Answer: a
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}.
advertisement

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

Answer: b
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

Answer: a
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}}.
advertisement

8. Cardinality of the power set of {0, 1, 2 . . ., 6} is _________
a) 1024
b) 4096
c) 512
d) 2048
View Answer

Answer: d
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
View Answer

Answer: b
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.
advertisement

10. If set A={Φ} then P(A) is ___________
a) {Φ}
b) {{Φ}}
c) {Φ, {Φ}}
d) Φ
View Answer

Answer: c
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.

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

advertisement
advertisement
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter