Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let . The total number of unordered pairs of disjoint subsets of<img alt="S" src="http

Let S=\{1,2,3,4\}. The total number of unordered pairs of disjoint subsets ofSis equal to

Option: 1

25


Option: 2

34


Option: 3

42


Option: 4

41


Answers (1)

best_answer

Let A and B be two subsets of S. If \mathrm{x \in S}, then \mathrm{x } will not belong to \mathrm{A \cap B } if x belongs to at most one of A, B. Thus can happen in 3 ways.

Thus, there are \mathrm{3^{4}=81} subsets of \mathrm{S} for which \mathrm{A \cap B=\phi}.
Out of these there is just one way for which \mathrm{A=B=\phi}.

As we, are interested in unordered pairs of disjoint sets, the number of such subsets is

\frac{1}{2}\left(3^{4}-1\right)+1=41.

Posted by

Ajit Kumar Dubey

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

NTA Exams 2025 Live: NEET UG date, registration form soon at neet.nta.nic.in; UGC NET revised schedule out
anam-khan

Is it difficult to get into NIT Durgapur? JEE Main cut-offs for BTech programmes
anam-khan

JEE Main Deleted Syllabus 2025: Topics to skip this year; why no optional questions?

Latest Question