Question

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

(ii) $(a,b)\in R\Rightarrow (b,a)\in R$.

Answer 1

Given: $R=\left\{\right(a,b):a,b\in N\text{and}a=b^2\}$

If $(a,b)\in R,$ then

$a=b^2$ ...$\left(1\right)$

When $(b,a)\in R$

$b=a^2$

From equation $\left(1\right)$, we get

$b=b^4$

$\Rightarrow b(b^3-1)=0$

$\Rightarrow b=0,1$

As relation is defined from $N$ to $N$, so $b=1$

So, $(a,b)\in R\Rightarrow (b,a)\in R$ is not correct for all possible $(a,b)\in R$

Hence, the given statement is False.