Let `A={1,\ 2,\ 3}` and consider the relation `R={(1,\ 1),\ (2,\ 2),\ (3,\ 3),\ (1,\ 2),\ (2,\ 3),\ (1,\ 3)}` . Then, `R` is (a) reflexive but not symmetric (b) reflexive but not transitive (c) symmetric and transitive (d) neither symmetric nor transitive

Answer

a) reflexive but not symmetric

Explanation

Relation R is reflexive relation over Set A as Every element of A is related to itself in R.

Relation R is not symmetric as `(1,2)` is in R but `(2,1)` is not in R.

Relation R is also not a transitive

As for a,b,c in A

If `(a,b)`is in R and `(b,c)`is in R, then `(a,c)` is also in R.