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

Explanation

Every set is a subset of itself.
`therefore ` For each `A in p(x) ""_AR_A`
`rArr ` R is reflexive
Again ,let `""_A R_B` where A,B `in ` P(x)
`rArr A sub B`
`rArr B cancelsub A rArr ""_BR_A`
`therefore` R is not symetric
`because ` R is not symmetric
`therefore` R is not an equivalence relation.