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

A is a set containing n elements. A subset P of A is chosen. The set A is reconstructed by replacing the elements of P. A subset Q of A is again chosen. The number of ways of choosing P and Q so that PQ=ϕ is:

A
3n
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
32n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
22n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 3n
Let x1ϵA
Then the following case arises.
Case I
x1ϵP and x1ϵQ ...(not favorable).
Case II
x1P and x1ϵQ ...(favorable).
Case III
x1P and x1Q ...(favorable).
Case Iv
x1P and x1Q ...(favorable).
Hence we have 3 favorable cases.
Therefore the number of choosing P and Q such that PQ=ϕ
=3n

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Set Operation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon