Prove or disprove:

If $M, N$ are R-module and for all $P$ R-module $Hom(M,P) \simeq Hom(N,P)$ then $M\simeq N$

Let $R$ be a commutative ring and let $M$ and $N$ be two $R$-modules. Suppose that for every $R$-module $P$, the modules $Hom_R(M,P)$ and $Hom_R(N,P)$ are isomorphic. Is it true that $M$ and $N$ are isomorphic?

If $M, N$ are R-module is it true that if $Hom(M,P) \simeq Hom(N,P)$ for all $P $ then $M\simeq N$ ?

Prove or disprove:

If $M, N$ are R-module and for all $P$ R-module $Hom(M,P) \simeq Hom(N,P)$ then $M\simeq N$