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Question

Let R be a relation on the set N be defined by {(x,y)|x,yϵN,2x+y=41}. Then R is

A
Reflexive
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B
Symmetric
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C
Transitive
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D
None of these
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Solution

The correct option is D None of these
On the set N of natural numbers,
R={(x,y);x,yϵN,2x+y=41}.
Since (1,1)/ϵR as 2.1+1=341. So, R is not reflexive. Where R is the Relation.
(1,39)ϵR but (39,1)/ϵR. So R is not symmetric (20, 1)
(1,39)ϵR. But (20,39)/ϵR, So R is not transitive.

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