Difference between revisions of "GATE2010 q3"

Revision as of 23:06, 13 July 2014

What is the possible number of reflexive relations on a set of $5$ elements?

(A) $2^{10}$

(B) $2^{15}$

(C) $2^{20}$

(D) $2^{25}$

Solution by Happy Mittal

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.