In order that a relation $R$ defined in a non-empty set $A$ is an equivalence relation, it is sufficient that $R$

Q. In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R .......................

Q. In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation.
It is sufficient, if $R$

Q. Assertion :The relation $R=A\times A$ ( where $A$ is non empty set) is an equivalence relation. Reason: Relation $R=A\times A$ satisfies the property reflexivety , symmetricity and transitivity.

Q. Give a non-empty set $X$. Consider $P\left(X\right)$, which is the set of all subsets of $X$. Define the relation $R$ in $P\left(X\right)$ as follows:
For subsets $A$ and $B$ in $P\left(X\right)$, $ARB$ if $A\subset B$, is $R$ an equivalence relation on $P\left(X\right)$?
Justify your answer.

Q.

Given a non-empty set X. Consider P(X), which is the set of all subset of X. Defined the relation R in P(X) as follows:
For subsets A and B in P(X),ARB if and only if $A\subset B$. Is R an equivalence relation on P(X)? Justify your answer.