Let A = { 1 , 2 , 3 } . The number of equivalence relations containing ( 1 , 2 ) is (a) 1 (b) 2 (c) 3 (d) 4

Question

Let A = { 1 , 2 , 3 } . The number of equivalence relations containing ( 1 , 2 ) is (a) 1 (b) 2 (c) 3 (d) 4,

MARKS App · Accepted Answer

There are two equivalence relations containing $(1,2)$. i.e. $\mathrm{R}_1=\{(1,2),(1,1),(2,2),(3,3),(2,1)\}$ and
$$
R_2=\{(1,2),(1,1),(2,2),(3,3),(2,1),(1,3),(3,1),(2,3),(3,2)\}
$$

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