# Math Help - Proving identities of sets

1. ## Proving identities of sets

Hello people!

I'm having a hard time with these few problems.
It's been ages since i've done anything with sets so I have pretty much forgotton everything.
I've been battling with these problems for 3 days now and to be honest haven't got nowhere so I'm pretty much in trouble since deadline for 'em is tomorrow

Any you guys could give a hand with these? Would really really appreciate it!

Proof identity of sets;
(problems in attached image)

2. try to draw a venn diagram.

3. Problem is that I have to prove them with definitions(right word?) and venn-diagrams are forbidden as final answers.

4. Here is some help on these.
$\begin{gathered}
\left( {x,y} \right) \in A \times \left( {B \cup C} \right) \hfill \\
\left[ {x \in A} \right] \wedge \left[ {y \in \left( {B \cup C} \right)} \right] \hfill \\
\left[ {x \in A} \right] \wedge \left[ {y \in B \vee y \in C} \right] \hfill \\
\end{gathered}$

$\begin{gathered}
\left[ {\left( {x \in A} \right) \wedge \left( {y \in B} \right)} \right] \vee \left[ {\left( {x \in A} \right) \wedge \left( {y \in C} \right)} \right] \hfill \\
\left[ {(x,y) \in \left( {A \times B} \right)} \right] \vee \left[ {(x,y) \in \left( {A \times C} \right)} \right] \hfill \\
\end{gathered}$

Please see if you can continue.