Question

A ={1,2,3,4,5,6}
On A, R be a relation given by R = {(1,2),(2,1),(1,1)}.
Check whether R is symmetric or transitive

Answer 1

Answer:

R is symmetric but not transitive

(1,2) belongs to R

(2,1) belongs to R ; i.e, (a,b) belongs to R and (b,a) also belongs to R

Therefore, R is symmetric relation

(1,2) belongs to R

(2,1) belongs to R

(1,1) belongs to R ; i.e, (a,b) belongs to R and (b,a) belongs to R but (b,c) doesn't belongs to R.

Therefore, R is not a transitive relation.