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
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a
Reflexive and symmetric
b
Symmetric only
c
Symmetric and transitive
d
Reflexive only
answer is B.
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Detailed Solution
GCD of (3,3)=3R is not reflexive If (a,b)∈R⇒GCD of (a,b)=2 then GCD of (b,a)=2 R is symmetrica,b,(b,c)∈Rbut a,c∉R ∵8,10,10,12∈R but 8,12∉RR is not transitive