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August 28th, 2017, 12:34 PM   #1
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Question 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 12:47 PM.
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August 28th, 2017, 12:53 PM   #2
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The ⋃ and ⋂ operations are each commutative (for any pair of sets). What other rules could you use?
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August 28th, 2017, 01:53 PM   #3
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B-A is equivalent to B∩cA.
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September 1st, 2017, 04:12 AM   #4
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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 04:33 AM.
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