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 A R_1 B if ( {\A} \cap {\B}^{ {\c}}) \cup ( {\B} \cap {\A}^9) =\emptyset and {\AR}_2 {\B} if {\A} \cup {\B}^{ {\c}}= {\B} \cup {\A}^{ {\c}}, \forall {\A}, {\B} \in {\P}( {\S}). Then : [1-Feb-2023 Shift 2]

Correct Answer is : both R1 and R2 are equivalence relations

both R_1 and R_2 are equivalence relations

only R_1 is an equivalence relation

only R_2 is an equivalence relation

both R_1 and R_2 are not equivalence relations

JEE Mains 1-Feb-2023 Shift 2 Solved Paper

Section: Mathematics

Question : 72 of 90

Marks: +1, -0

Let P(S) denote the power set of S={1,2,3,...,10}. Define the relations R1 and R2 on P(S) as AR1B if (A∩Bc)∪(B∩A9)=∅ and AR2B if A∪Bc= B∪Ac,∀A,B∈P(S). Then :

[1-Feb-2023 Shift 2]

both R1 and R2 are equivalence relations
only R1 is an equivalence relation
only R2 is an equivalence relation
both R1 and R2 are not equivalence relations

Validate

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