State the reason for the relation `R` in the set `{1, 2, 3}` given by `R={(1, 2), (2, 1)}` not to be transitive.

State the reason for the relation R on the set {1,2,3} given by R={(1,2),(2,1)} not to be transitive.

The relation in the set A = {1, 2, 3} given by R = {(2,3),(3,2),(1,1)} is:

Show that the relation R in the set {1,2,3} given by R={(1,2),(2,1)} is symmetric but neither reflexive nor transitive.

If a relation R on the set {1,2,3} be defined by R={(1,2)}, then R is:

Show that the relation R on the set A={1,2,3} given by R={(1,2),(2,1)} is symmetric but neither reflexive nor transitive.

Show that the relation R in the set {1, 2, 3} defined as: (a) R={(1,2),(2,1)} is symmetric, but neither reflexive nor transitive (b) R={(1,1),(2,2),(3,3),(1,2),(2,3)} is reflexive, but neither symmetric nor transitive (c ) R={(1,3),(3,2),(1,2)} is transitive, but neither reflexive nor symmetric.

Show that the relation R in the set {1,2,3} given by R={(1,1),(2,2),(3,3),(1,2),(2,3)} is reflexive but neither symmetric nor transitive.

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b):|a-b| is even }, is an equivalence relation.