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Question

R is relation over the set of integers and it is given by (x, y) ϵ R R |x - y| 1. Then, R is

A
Reflexive and transitive
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B
reflexive and symmetric
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C
Symmetric and transitive
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D
an equivalence relation
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Solution

The correct option is B reflexive and symmetric
As (x,x) ϵ R |xx| 1
0 1 (True),
Thus, reflexive.
As (x,y) ϵ R |xy| 1
|yx||1 (y,x) ϵ R,
Thus, symmetric.
Again, (x, y) ϵ R and (y, z) ϵ R
|xy| 1 and |yz|1/|xz| 1
Not transitive

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