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

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Reflexive and symmetric

Symmetric only

Symmetric and transitive

Reflexive only

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detailed solution

Correct option is B

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

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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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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