Given a non empty set & 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 it A ⊂B. Then R is not

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Given a non empty set & 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 it A ⊂B.  Then R is not

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Since every set is a subset of itself, ARA for all A∈$$P(X)Therefore$$, .R is reflexive.  Let ARB⇒A⊂B .  This cannot be implied to B⊂A .  For instant, if $$A={1$$,$$2}$$ and $$B={1$$,$$2$$,$$3}$$, then it cannot be implied that B is related to A. Therefore, R is not symmetric.  Further if ARB and BRC , then A⊂B and B⊂C . ⇒ A⊂C⇒ ARCTherefore, R is transitive. Hence, R is not an equivalence relation since it is not symmetric

Given a non empty set & 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 it A $\subset$ B. Then R is not

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Given a non empty set & 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 it A ⊂B. Then R is not

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Given a non empty set & 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 it A $\subset$ B. Then R is not