$(8$ points$)$ Suppose that for two problems $x$ and $Y$ we have proven that $x{?}_{P}Y.$ Then which of the following must be true? Choose any$/$all that apply.

If $Y$ is easy $($i$.$e$.,$ there is poly$-$time algorithm to solve $Y),$ then $x$ is easy.

If $x$ is easy, then $Y$ is easy.

If $x$ is NP$-$hard, then $Y$ is also NP$-$hard.

If $Y$ is NP$-$hard, then $x$ is also NP$-$hard.