Question

Explain why every identity relation is equivalent.Give examples

Answer 1

The identity relation on set E is the set {(x, x) | $xϵE$}
$\begin{array}{cccc}ArelationRis\dots & if\dots & ArelationRis\dots & if\dots \\ reflexive& xRx& irreflexive& xRyimpliesx\ne y\\ symmetric& xRyimpliesyRx& antisymmetric& xRyandyRximpliesx=y\\ transitive& xRyandyRzimpliesxRz& & \end{array}$
An equivalence relation is a relation that is reflexive, symmetric, and transitive.
Transitivity is an attribute of all equivalence relations (along with symmetric and reflexive property). Identity relation is a prime example of an equivalence relation, so it satisfies all three properties.
If a = b and b = c then obviously a = c. The formal proof of this would depend on which foundations you are building and how the identity is defined.