Question

R is a binary relation on a set S and R is reflexive if and only if _______

(a) r(R) = R

(b) s(R) = R

(c) t(R) = R

(d) f(R) = R

The question was posed to me in semester exam.

The doubt is from Closure on Relations in division Relations of Discrete Mathematics

Answer 1

Correct option is (a) r(R) = R

The best I can explain: Let reflexive closure of R:r(R) = R. If R is reflexive, it satisfies all the condition in the definition of reflexive closure. So, a reflexive closure of a relation is the smallest number of reflexive relation contain in R. Hence, R = r(R).