Prove that relation R is an equivalence relation

Question

Let $A$ be a finite set (not empty) and $B$ a subset of $A$:

How to prove that relation

$R = \{(f,g) \mid f,g \in \{1,0\}^A, B \in P(\{x \in A \mid f(x)=g(x)\})\} $

is an equivalence relation?

Equivalence relation means that it must be a reflexive relation, a symmetric relation and a transitive relation.

How i can prove those three statements?

Thanks