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August 8th, 2012, 08:39 AM   #1
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Set theory

How do you prove this?

=(A\cap B) \cap (A\cap C)'" />

This is how i am approaching it but im stuck a one point:

So lets have " />, which means that and" />, this also means that and , Then we have: and so . But what do i do with the ? Also my teacher said we have to show for both LHS and RHS.

If i start with RHS this time it becomes weirder. let , this means that and which gives , and . How is this possible when and we have . Im so confused with this proof.

Similarly how do you prove:

Can anyone help me understand this clearly?? will appreciate any help.
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August 8th, 2012, 09:18 AM   #2
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Re: Set theory

Use De'Morgan's law.
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August 8th, 2012, 09:26 AM   #3
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Re: Set theory

Hello, gaussrelatz!

Quote:







Quote:





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August 8th, 2012, 09:35 AM   #4
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Re: Set theory

Thank you very much for the help. Ok i see the proof using the algebra of sets, could you also please give me a proof using the elements for example, by beginning with : let etc... and show from there. I tried to prove it set algebraically but my teacher said i should be using the proof as i mentioned like above in my post.
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