First slide

Relations XII

Question

$On the set ' N' of all natural numbers, define the relation ' R' by aRb if the G.C.D of a and$ b is 2. Then R is

Easy

A

Reflexive and symmetric
B

Symmetric only
C

Symmetric and transitive
D

Reflexive only

Solution

$GCD of (3, 3) = 3$
R is not reflexive

$If (a, b) \in R \Rightarrow G C D of (a, b) = 2$
$then GCD of (b, a) = 2$
R is symmetric
$(a, b), (b, c) \in R$
but $(a, c) \notin R$ $(∵ (8, 10), (10, 12) \in R b u t (8, 12) \notin R)$
R is not transitive

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