August 8th, 2012, 08:39 AM  #1 
Senior Member Joined: Sep 2011 Posts: 140 Thanks: 0  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. 
August 8th, 2012, 09:18 AM  #2 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Set theory
Use De'Morgan's law.

August 8th, 2012, 09:26 AM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Set theory Hello, gaussrelatz! Quote: Quote:  
August 8th, 2012, 09:35 AM  #4 
Senior Member Joined: Sep 2011 Posts: 140 Thanks: 0  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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