Difference between revisions of "GATE2010 q3"

Revision as of 17:34, 15 April 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. So from rest of the 20 elements, we have choice whether to include them or not. So we have $2^{20}$ possible reflexive relations. So option (C) is correct.