if A is in P and B is NP, is A ≤p B?
If $B$ is neither empty nor the universal set, then the reduction can be performed and is trivial. 

You need to have two strings $w_1 \in B$ and $w_2 \notin B$. In the reduction of membership problem $(A,x)$, we trivially solve the membership in $A$ in polynomial time: if $x \in A$ then return $w_1$ else $w_2$.