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Let S be the set of all subsets of first 10 natural numbers. If a relation R is defined on set S such that (A, B) $\in$ R if $A \cap B \neq ϕ; w h e r e A, B \in S$ , then R is

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Symmetric and Transitive only

Symmetric and reflexive only

Symmetric only

Reflexive only

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detailed solution

Correct option is C

ϕ∩ϕ=ϕ⇒(ϕ,ϕ)∉R∴R is not reflexive Clearly R is symmetric but not transitive ( if A ={1,2,3} , B={ 3, 4 } , C = {4,5,6} then A∩B ={3} ≠ ∅ and B ∩C ≠∅ but A ∩C =∅ . so not transitive )

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Let S be the set of all subsets of first 10 natural numbers. If a relation R is defined on set S such that (A, B)∈ R if A∩B≠ϕ;where A,B∈S, then R is

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Ready to Test Your Skills?

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Let S be the set of all subsets of first 10 natural numbers. If a relation R is defined on set S such that (A, B) $\in$ R if $A \cap B \neq ϕ; w h e r e A, B \in S$ , then R is