R = {(x, y) : x and y live in the same locality}

Question

Determine whether each of the follow relations are reflexive, symmetric and transitive:

Relation R in the set A of human beings in a town at a particular time given by

R = {(x, y) : x and y live in the same locality}

Answer 1

R is reflexive as x and x work at the same place

R is symmetric as x and y work at the same place

⇒ y and x work at the same place R is transitive as transitivity does not contradict.