JEE Main · MathematicsMedium

$Let A = {1, 2, 3} . How many relations on A are both reflexive and symmetric?$

A. $8$
B. $16$
C. $4$
D. $64$

Show correct answer & step-by-step solution

Correct answer: A — $8$

Solution

Reflexive requires {(1, 1), (2, 2), (3, 3)} . The remaining pairs are {(1, 2), (2, 1), (1, 3), (3, 1), (2, 3), (3, 2)} . We choose subsets of {(1, 2), (1, 3), (2, 3)} and include their symmetric counterparts, giving 2^{3} = 8 relations.

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