PrepRung
Sign inSign up free

NDA 2020 Maths · Mathematics · Sets, Relations and Functions · hard

The number of symmetric relations on a set containing 4 elements is

Single correct option

The number of symmetric relations on a set containing 4 elements is
  1. A. 1024
  2. B. 256
  3. C. 4096
  4. D. 64
Show answer and solution

Answer: (A) 1024

A symmetric relation is fixed by choosing, for each of the 4 diagonal pairs (a,a)(a,a) and each of the (42)=6\binom42=6 unordered pairs {a,b}\{a,b\}, whether it is included. That gives 4+6=104+6=10 independent choices, so 210=10242^{10}=1024. The value 4096 =212=2^{12} wrongly counts (a,b)(a,b) and (b,a)(b,a) independently.
Report a mistake

Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake