Q.

Let n  be a positive integer. if  R is a relation defined on Z as xRyxy is divisible by n,  then R is

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a

reflexive

b

symmetric

c

transitive

d

equivalence

answer is D.

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Detailed Solution

xx,yy and x divisible by n  it is reflexive

If xy  is divisible n  then (yx)  it is divisible by n  it is symmetric

xy  is divisible by n,yz   is divisible  by n  then xz  is divisible by n  it is transitive

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Let n  be a positive integer. if  R is a relation defined on Z as xRy⇔  x−y  is divisible by n,  then R is