Question

show that the realtion R in the set {1,2,3} given by R={(1,2),(2,1)} is symmetric but neither reflexive nor transitive​

Answer 1

Step-by-step explanation:

Relation is not reflexive because

(a, a) not belongs to R

which means (1,1)(2,2)(3,3) not belong to R

so this relation is not reflexive

relation is symmetric because

(a, b) and (b, a) belong to R

(1,2) belong to R (2,1) also belong to R

so this R is symmetric

not transitive

(a, b) ,(b,c) belongs to R but (a, c) not belong to R

(1,2)(2,1) belong to R but (1,1) not belong to R

thus this is not transitive