An empty relation on set A is a subset of the cartesian product $A \times A$ .

True

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False

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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:

Empty relation on a set A is the subset of Cartesian product $A \times A$

P

Q

P \times Q .

P

Q

P \times Q .

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An empty relation on set A is a subset of the cartesian product A×A.