Question

The number of non-empty equivalence relations on the set {1, 2, 3} is :

(1) 6

(2) 7

(3) 5

(4) 4

Answer 1

Correct option is (3) 5 

Let R be the required relation

\(\mathrm{A}=\{(1,1)(2,2),(3,3)\}\)

(i) \( |\mathrm{R}|=3, \text{when} \mathrm\ {R}=\mathrm{A}\)

(ii) \(|\mathrm{R}|=5, e.g. \mathrm{R}=\mathrm{A} \cup\{(1,2),(2,1)\}\)

Number of R can be [3]

(iii) \(\mathrm{R}=\{1,2,3\} \times\{1,2,3\}\)