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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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