wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

For a set A consider the following statements:

1.AP(A)=P(A)

2.{A}P(A)=A

3.P(A)-{A}=P(A) where P denotes power set.

Which of the statements given above is/are correct?


A

1Only

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

2 Only

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

3 Only

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

1,2,3

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B

2 Only


Explanation for the correct option:

Power set is the collection of all the subsets of the set A.

Let A=1,2 and A=1,2

P(A)=1,2,1,2,ϕ

Now,

Option (B): {A}P(A)=A

AP(A)=1,21,2,1,2,φ

=1,2=A

Explanation for the incorrect option :

Option (A): AP(A)=P(A)

AUP(A)P(A) because Ais subset of Powerset P

Option (C) : P(A)-{A}=P(A)

P(A)-{A}={{1},{2},{1,2},{ϕ}}-{1,2}={{1},{2},{ϕ}}P(A)

Therefore statement (2) is correct.

Hence, Option ‘B’ is correct.


flag
Suggest Corrections
thumbs-up
5
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Sets and Their Representations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon