Question

The relation $R=\{(1,1),(2,2)(3,3)\}$ on the set $A=\{1,2,3\}$ is

• A. symmetric only
• B. reflexive only
• C. an equivalence relation
• D. transitive only

Answer 1

The correct option is C an equivalence relation

The relation R is reflexive relation over set A as every element of set A is related to itself in relation R.

The relation R is also symmetric as for a,b in A, if (a,b) is in R, then (b,a) is also in R .

The relation R is also 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.

Thus relation R is an equivalence relation, So C is correct answer .