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Return to GATE2010 q3.
What is the possible number of reflexive relations on a set of $5$ elements?
(A) $2^{10}$
(B) $2^{15}$
(C) $2^{20}$
(D) $2^{25}$
Consider a table of size $5*5$ in which each possible pair is listed. In a reflexive relation, we must include all $5$ diagonal elements. From rest of the $20$ elements, we have choice whether to include them or not. Thus we have $2^{20}$ possible reflexive relations. So option (C) is correct.
GATECSE