Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
$(a, a) \in R$,for all $a \in N$

(B) The relation is defined as $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$.
For the statement $(a, a) \in R$ to be true for all $a \in N$,the condition $a = a^2$ must hold for every natural number $a \in N$.
Consider $a = 2$. Since $2 \in N$,we check if $(2, 2) \in R$.
Here,$a = 2$ and $b = 2$. The condition $a = b^2$ becomes $2 = 2^2$,which is $2 = 4$.
Since $2 \neq 4$,the pair $(2, 2) \notin R$.
Therefore,the statement $(a, a) \in R$ for all $a \in N$ is false.