- #1
MartianVision
- 3
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Homework Statement
The question is, simplify this equation:
(A ∪ B ∪ C) ∩ ((A ∩ B) ∪ C)
The correct answer is (A ∩ B) ∪ C
Homework Equations
We have been given the commulative, associative, distributive, identity, complement and idempotent laws and DeMorgan's laws, and I researched the absorption laws myself.
The Attempt at a Solution
I tried doing:
(A ∪ B ∪ C) = x
(A ∩ B) = y
C = z <-- ((I know this isn't necessary, but thought it might make things easier)
From there I did:
(A ∪ B ∪ C) ∩ ((A ∩ B) ∪ C) = x ∩ (y ∪ z)
= (x ∪ y) ∩ (x ∪ z)
= ((A ∪ B ∪ C) ∪ (A ∩ B)) ∩ ((A ∪ B ∪ C) ∪ C)
= (A ∪ B ∪ C) ∩ (A ∪ B ∪ C) <-- I'm guessing I went wrong here, but I'm not too sure?
= (A ∪ B ∪ C)
I've tried a few other methods, but this one is the one that makes most sense.When I try to draw a venn diagram, I just don't understand how it isn't (A ∪ B ∪ C). I'm completely stumped :/