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
Answer: Option B
:
B
As (x,x) ϵ R ⇒ |x−x|≤ 1
⇒ 0 ≤ 1 (True),
Thus, reflexive.
As (x,y) ϵ R ⇒ |x−y|≤ 1
⇒|y−x||≤1⇒ (y,x) ϵ R,
Thus, symmetric.
Again, (x, y) ϵ R and (y, z) ϵ R
⇒|x−y|≤ 1 and |y−z|1/⇒|x−z|≤ 1
∴ Not transitive
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:
B
As (x,x) ϵ R ⇒ |x−x|≤ 1
⇒ 0 ≤ 1 (True),
Thus, reflexive.
As (x,y) ϵ R ⇒ |x−y|≤ 1
⇒|y−x||≤1⇒ (y,x) ϵ R,
Thus, symmetric.
Again, (x, y) ϵ R and (y, z) ϵ R
⇒|x−y|≤ 1 and |y−z|1/⇒|x−z|≤ 1
∴ Not transitive
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