Let R be a relation on Ndefined by $$R={(m$$,$$n)$$:m,n∈N and $$m=n2}$$ Which of the following is true.

Correct option is 4none of these

Questions

Let $R$ be a relation on $N$ defined by $R = {(m, n) : m, n \in N$ and $m = n^{2}}$ Which of the following is true.

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(n,n)∈R. ∀n∈N

(m,n)∈R⇒(n,m)∈R

(m,n)∈R,(n,p)∈R⇒(m,p)∈R

none of these

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detailed solution

Correct option is D

(n,n) ∈ R only for n=1m=n2 ⇒n=m2 unless m=n=1m=n2 and n=p2 ⇒m=p2 for m,n,p≠1hence (a),(b),(c) none is true.

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Let R be a relation on Ndefined by R={(m,n):m,n∈N and m=n2} Which of the following is true.

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Let $R$ be a relation on $N$ defined by $R = {(m, n) : m, n \in N$ and $m = n^{2}}$ Which of the following is true.