Let R be a relation from N to N defined by R =

Solution:

Given: R = [(a, b) : a, b ∈ N and a = b2]

(i) (a, a) ∈ R for all a ∈ N.

Here $2 \in \mathrm{N}$ hut? $\neq 2^{2}$

$\therefore(2,2) \notin \mathrm{R}$

False

(ii) $(a, b) \in \mathrm{R} \Rightarrow(b, a) \in \mathrm{R}$

$\because 4=2^{2}$

$(4,2) \in \mathrm{R}$, but $(2,4) \notin \mathrm{R}$

False

(iii) $(a, b) \in \mathbf{R}$ and $(b, c) \in \mathbf{R} \Rightarrow(a, c) \in \mathbf{R}$

$\because 16=4^{2}$ and $4=2^{2}$

$\therefore(16,4) \in \mathrm{R}$ and $(4,2) \in \mathrm{R}$

Here,

$(16,2) \notin \mathrm{R}$

False