Mark the tick against the correct answer in the following:

Solution:

According to the question ,

Given set $S=\{x, y, z\}$

And $R=\{(x, x),(y, y),(z, z)\}$

Formula

For a relation $R$ in set $A$

Reflexive

The relation is reflexive if $(a, a) \in R$ for every $a \in A$

Symmetric

The relation is Symmetric if $(a, b) \in R$, then $(b, a) \in R$

Transitive

Relation is Transitive if $(a, b) \in R \&(b, c) \in R$, then $(a, c) \in R$

Equivalence

If the relation is reflexive, symmetric and transitive, it is an equivalence relation.

Check for reflexive

Since, $(x, x) \in R,(y, y) \in R,(z, z) \in R$

Therefore, $R$ is reflexive ....... (1)

Check for symmetric

Since,$(x, x) \in R$ and $(x, x) \in R$

$(y, y) \in R$ and $(y, y) \in R$

$(z, z) \in R$ and $(z, z) \in R$

Therefore, $\mathrm{R}$ is symmetric ....... (2)

Check for transitive

Here, $(x, x) \in R$ and $(y, y) \in R$ and $(z, z) \in R$

Therefore, $\mathrm{R}$ is transitive ....... (3)

Now, according to the equations (1), (2), (3)

Correct option will be (D)