Let `A = {1, 2, 3}`. Then number of equivalence relations containing (1, 2) is (A) 1 (B) 2 (C) 3 (D) 4

Answer

a) 1

Explanation

`A={1,2,3}`



For equivalence relation containing` (1,2)`

For symmetric, it must consists `(1,2) and (2,1)`.

For transitivity, it must consists` (1,3) and (3,2) and (1,2),(2,1),(2,3),(3,1) `

For reflexivity, it must consists `(1,1) and (2,2),(3,3)`



Rightarrow `{R}={(1,1),(2,2),(2,3),(3,3),(1,2)(1,3),(2,1),(3,1),(3,1)}`


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