If $K$ is algebraic, then every subset of $\mathbb A^n(K)$ is algebraic

If $K$ is algebraic, then every subset of $\mathbb A^n(K)$ is algebraic

I'm trying to prove that if $K$ is a finite field, then every subset of
$\mathbb A^n(K)$ is algebraic. I know that if $K$ is finite, then every
element of $K$ is algebraic, i.e., for every $a\in K$ there is a
polynomial $f\in K$ such that $f(a)=0$, but this didn't help me to solve
the question. I almost sure that we have to use this to solve this
question.
I need help.
Thanks in advance.