Question:
If R is a relation on Z and is given by R = x, y : x − y ≤ 1 Then R is (a) Reflexive and Transitive (b) Reflexive and Symmetric (c) Symmetric and Transitive (d) Equivalence Relation
Answer:
, for relation on Z
As,
,
thus R is reflexive.
But, let
,
then
,
but
, thus not symmetric.
Again, let
, then
i.e.,
i.e., not ≤1 . Hence, not transitive.
Hence, no given option is correct.
It should be only reflexive.
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