Let P(S) denote the power set of S=\1,2,3,., 10. Define the relations R₁ and R₂ on P(S) as AR₁ ~B if (A B^(c)) (B A^(c))= and AR₂ ~B if A B^(c)=B A^(c), A, B P(S). Then:

(C) both R₁ and R₂ are equivalence relations

(A) only R₂ is an equivalence relation

(B) both R₁ and R₂ are not equivalence relations

(D) only R₁ is an equivalence relation

Sets, Relations and Functions: JEE Main 2023 Mathematics question

JEE Main 2023 · 1 Feb, Evening shift · Q5384

JEE Main 20231 Feb, Evening shiftMathematicsHardSets, Relations and Functions168× since 2002

Let

P(S)

denote the power set of

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

. Define the relations

R_{1}

and

R_{2}

P(S)

\mathrm{AR}_{1} \mathrm{~B}

\left(\mathrm{A} \cap \mathrm{B}^{\mathrm{c}}\right) \cup\left(\mathrm{B} \cap \mathrm{A}^{\mathrm{c}}\right)=\emptyset

and

\mathrm{AR}_{2} \mathrm{~B}

\mathrm{A} \cup \mathrm{B}^{\mathrm{c}}=\mathrm{B} \cup \mathrm{A}^{\mathrm{c}}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{S})

. Then :

JEE Main 2023 · 1 Feb, Evening shift · Q5384

JEE Main 20231 Feb, Evening shiftMathematicsHardSets, Relations and Functions168× since 2002

Let

P(S)

denote the power set of

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

. Define the relations

R_{1}

and

R_{2}

P(S)

\mathrm{AR}_{1} \mathrm{~B}

\left(\mathrm{A} \cap \mathrm{B}^{\mathrm{c}}\right) \cup\left(\mathrm{B} \cap \mathrm{A}^{\mathrm{c}}\right)=\emptyset

and

\mathrm{AR}_{2} \mathrm{~B}

\mathrm{A} \cup \mathrm{B}^{\mathrm{c}}=\mathrm{B} \cup \mathrm{A}^{\mathrm{c}}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{S})

. Then :