Let denote the power set of . Define the relations and on as if and if . Then...

(i) for reflexive (ii) symmetric It is symmetric (iii) Transitive is transitive is equivalence relation. Sim...

Let P(S) denote the power set of S = { 1,2,3,...,10}. Define the relations R_{1} and R_{2} on P(S) as AR_{1}B if ( A cap B^{C} ) cup ( B cap A^{C} ) = phi and AR_{2}B if cup B^{C} = B cup A^{C},forall A,B in P(S). Then: Relation (Mathematics)

Let

P(S)

denote the power set of

S = \{ 1,2,3,\ldots,10\}

. Define the relations

R_{1}

and

R_{2}

P(S)

AR_{1}B

\left( A \cap B^{C} \right) \cup \left( B \cap A^{C} \right) = \phi

and

AR_{2}B

\cup B^{C} = B \cup

A^{C},\forall A,B \in P(S)

. Then

both

R_{1}

and

R_{2}

are not equivalence relations

only

R_{2}

is an equivalence relation

only

R_{1}

is an equivalence relation

both

R_{1}

and

R_{2}

are equivalence relations