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Math Help - Proving identities of sets

  1. #1
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    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!

    Ps. Sorry for bad english


    Proof identity of sets;
    (problems in attached image)
    Attached Thumbnails Attached Thumbnails Proving identities of sets-problems.jpg  
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  2. #2
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    try to draw a venn diagram.
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  3. #3
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    Problem is that I have to prove them with definitions(right word?) and venn-diagrams are forbidden as final answers.
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  4. #4
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    Here is some help on these.
    \begin{gathered}<br />
  \left( {x,y} \right) \in A \times \left( {B \cup C} \right) \hfill \\<br />
  \left[ {x \in A} \right] \wedge \left[ {y \in \left( {B \cup C} \right)} \right] \hfill \\<br />
  \left[ {x \in A} \right] \wedge \left[ {y \in B \vee y \in C} \right] \hfill \\ <br />
\end{gathered}
    \begin{gathered}<br />
  \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 \\<br />
  \left[ {(x,y) \in \left( {A \times B} \right)} \right] \vee \left[ {(x,y) \in \left( {A \times C} \right)} \right] \hfill \\ <br />
\end{gathered}
    Please see if you can continue.
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