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