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R is a relation on the set Z of integers...

`R` is a relation on the set `Z` of integers and it is given by `(x ,\ y) in RhArr|x-y|lt=1.` Then, `R` is (a) reflexive and transitive (b) reflexive and symmetric (c) symmetric and transitive (d) an equivalence relation

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The correct Answer is:
b) reflexive and symmetric
Let {x} be a element in {Z},
then `|x-x|=0 leq 1.`
So ` forall z in ZZ `is related to itself,
Thus R is a reflexive relation.

Let x, y be `2` element in` ZZ`
such that` |x-y| leq 1`, then` |y-x| leq 1.`
So,` x R y Leftrightarrow y R x`
`therefore` R is a symmetric relation .

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