JEE Mains · Maths · STD 12 - 1. relation and function
Let \(P ( S )\) denote the power set of \(S =\{1,2,3, \ldots, 10\}\). Define the relations \(R_1\) and \(R_2\) on \(P(S)\) as \(A R_1 B\) if \(\left( A \cap B ^{ c }\right) \cup\left( B \cap A ^{ c }\right)=\varnothing\) and \(AR _2 B\) if \(A \cup B ^{ c }=\) \(B \cup A ^{ c }, \forall A , B \in P ( S )\). Then :
- A both \(R_1\) and \(R_2\) are equivalence relations
- B only \(R_1\) is an equivalence relation
- C only \(R_2\) is an equivalence relation
- D both \(R_1\) and \(R_2\) are not equivalence relations
Answer & Solution
Correct Answer
(A) both \(R_1\) and \(R_2\) are equivalence relations
Step-by-step Solution
Detailed explanation
\(S=\{1,2,3, \ldots \ldots .10\}\) \(P ( S )=\) power set of \(S\) \(AR , B \Rightarrow( A \cap \overrightarrow{ B }) \cup(\overrightarrow{ A } \cap B )=\phi\) \(R 1\) is reflexive, symmetric For transitive…
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