Question

Consider the binary relation, A = {(a,b) | b = a – 1 and a, b belong to {1, 2, 3}}. The reflexive transitive closure of A is?

(a) {(a,b) | a >= b and a, b belong to {1, 2, 3}}

(b) {(a,b) | a > b and a, b belong to {1, 2, 3}}

(c) {(a,b) | a <= b and a, b belong to {1, 2, 3}}

(d) {(a,b) | a = b and a, b belong to {1, 2, 3}}

This question was addressed to me in exam.

I would like to ask this question from Types of Relations in division Relations of Discrete Mathematics

Answer 1

The correct choice is (a) {(a,b) | a >= b and a, b belong to {1, 2, 3}}

To elaborate: By definition of Transitive closure we have that a is related to all smaller b (as every a is related to b – 1) and from the reflexive property a is related to a.