Let X be a $$non-empty$$ set and $$P(X)$$ be the set of all subsets of X. For A,B ∈ $$P(X)$$, ARB if and only if A∩$$B=$$∅ then the relation

Correct option is 2Ris symmetric

Questions

Let $X$ be a non-empty set and $P (X)$ be the set of all subsets of $X$ . For $A, B \in P (X), A R B$ if and only if $A \cap B = \emptyset$ then the relation

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R is reflexive

Ris symmetric

R is transitive

Ris an equivalence relation

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detailed solution

Correct option is B

A∩A=A≠ϕ if A≠ϕ, So R is not reflexive.A∩B=∅⇒B∩A=∅ARB⇒BRA⇒R is symmetricNote R is not transitive and not an equivalence relation.

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Let X be a non-empty set and P(X) be the set of all subsets of X. For A,B ∈ P(X), ARB if and only if A∩B=∅ then the relation

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Let $X$ be a non-empty set and $P (X)$ be the set of all subsets of $X$ . For $A, B \in P (X), A R B$ if and only if $A \cap B = \emptyset$ then the relation