Let $R=\{(a,b):a,b\in \mathbb{N}\text{ and }{a}^2=b\}$. Which property does the relation $R$ satisfy?

Let's test the properties:Reflexive: For all $a\in \mathbb{N}$, $(a,a)\in R⟹a^2=a$. This is only true for $a=1$. Since it doesn't hold for $a=2$ ($2^2\ne 2$), it is not reflexive.Symmetric: If $(a,b)\in R$, then $(b,a)\in R$. If $a=2,b=4$, then $2^2=4$ (belongs to $R$). But $4^2\ne 2$, so $(4,2)\notin R$. It is not symmetric.Transitive: If $(a,b)\in R$ and $(b,c)\in R$, then $(a,c)\in R$. If $a=2,b=4$ ($2^2=4$) and $b=4,c=16$ ($4^2=16$), then for transitivity $(2,16)$ must be in $R$. But $2^2\ne 16$. It is not transitive.Since it satisfies none of the above, Option D is correct.