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Given relation R={(x, y) :y=x+5, x<4, x, y ϵ N}. Where N is a set of natural numbers then:
Question

Given relation R={(x, y) :y=x+5, x<4, x, y ϵ N}. Where N is a set of natural numbers then:

A.

R is an equivalence relation.

B.

R is transitive but neither reflexive nor symmetric.

C.

R is reflexive but nether reflexive nor symmetric.

D.

R is symmetric & transitive but not reflexive.

Correct option is B

We have
R={(1, 6), (2, 7), (3, 8)}
Since (1,1)∉R. So, R is not reflexive
Since (1, 6)∈R but (6, 1)∉R
So, R is not symmetric.
R is transitive.

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