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August 28th, 2017, 11:34 AM  #1 
Member Joined: Sep 2014 From: Sweden Posts: 64 Thanks: 0  Set theory: simplify algebraic expressions
Hi! I'm new to the set theory and its algebraic expressions. So I don't really know how to apply the laws that exist. If we have the simple law: One of the commutative laws: $\displaystyle \displaystyle A \cup B = B \cup A$ Does this law apply to complements also? If we have $\displaystyle \displaystyle \mathsf{c}A$ for example? Or are laws that not include complement invalid for sets that don't are complements? My problem is this (the last expression is supposed to be A ⋃ (B  A) OBS! not the answer!): $\displaystyle \displaystyle A \cup (\mathsf{c}A \cap B) = $ $\displaystyle \displaystyle A \cup (B \cap \mathsf{c}A ) = $ $\displaystyle \displaystyle A \cup (B  A) = ?$ (I know you don't actually write B  A) Then I don't know how to go on from there. Last edited by skipjack; August 28th, 2017 at 11:47 AM. 
August 28th, 2017, 11:53 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1385 
The ⋃ and ⋂ operations are each commutative (for any pair of sets). What other rules could you use?

August 28th, 2017, 12:53 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,307 Thanks: 526 
BA is equivalent to B∩cA.

September 1st, 2017, 03:12 AM  #4 
Member Joined: Sep 2014 From: Sweden Posts: 64 Thanks: 0 
Could you show me an easy expression to simplify? Because I still not really get it . Not too easy expression though. Nevermind, actually clicked now Last edited by DecoratorFawn82; September 1st, 2017 at 03:33 AM. 

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algebraic, expressions, set, simplify, theory 
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