2nd one RHS is telling , for some R , there exists all I

But Say

$R=\left \{ 1,2 \right \}$

$I=\left \{ 3,4 \right \}$

Mapping here

$1\rightarrow 3$

$2\rightarrow 4$

Now, If we take, some R means only $1$, it doesnot have a mapping for $4.$

So, RHS fails