`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

Answer

b) reflexive and symmetric

Explanation

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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