First slide

Relations XII

Question

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.

Moderate

A

$(n, n) \in R . \forall n \in N$
B

$(m, n) \in R \Rightarrow (n, m) \in R$
C

$(m, n) \in R, (n, p) \in R \Rightarrow (m, p) \in R$
D

none of these

Solution

$(n, n) \in R$ only for $n = 1$
$m = n^{2} \Rightarrow n = m^{2}$ unless $m = n = 1$
$m = n^{2}$ and $n = p^{2}$ $\Rightarrow m = p^{2}$ for $m, n, p \neq 1$
hence $(a), (b), (c)$ none is true.

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