inclusion and concatenation of languages so for a homework assignment i need to prove the following:

We have arbitrary languages L1⊆∑1*, L2⊆∑2*, L3⊆∑3*, L4⊆∑4*

Prove that the followging is either true or false:

If L1 ∪ L2 ⊆ L3 ∩ L4, then L1◦L2 ⊆ L3◦L4 (◦ = concatenation)

Now i know this is true, but i don't know how to approach this problem...

Any tips on pointing me into the right direction are appreciated!
The assignment tests basic definitions (and some elementary set theory).

As you know, for arbitrary $L_1,L_2$, you have $L_1\cdot L_2 = \{ x\cdot y \mid x\in L_1, y\in L_2\}$. 

Now if $L_1\subseteq L_3$ and  $L_2\subseteq L_4$ then $L_1\cdot L_2 \subseteq L_3\cdot L_4$. This is rather clear, or if you want, can shown with elementary steps. Take any $z\in L_1\cdot L_2$, then $z=xy$ for $x\in L_1$ and $y\in L_2$. However, because of the inclusions, $z=xy$ for $x\in L_3$ and $y\in L_4$, thus $z\in L_3 \cdot L_4$.