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Kaleigh Beasley 2022-06-01 Answered
Can't solve ( A B ) C = ( A C ) ( B C ) = A ( B C ) any help?
I have discrete math exam and i can't quite figure out one example.
( A B ) C = ( A C ) ( B C ) = A ( B C )
i tried solving it like this and i got stuck: ( A B ) C = ( A B ¯ ) C ¯ , what next ?
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Answers (1)

Jakobe Yang
Answered 2022-06-02 Author has 5 answers
Step 1
More precisely, we have to apply the following properties of set operations ( A :   A ¯ is A's complement):
1. De Morgan's first law: A , B :   ( A B ) ¯ = A ¯ B ¯ .
2. Interpretation of set difference: A , B :   A B = A B ¯
Step 2
Now, we can rewrite you original equation as follows: ( A B ) C = [ by prop. (2) ] = ( A B ¯ ) C = ( A B ¯ ) C ¯ = = [ since set intersection is associative ] = = A ( B ¯ C ¯ ) = [ by prop. (1) ] = A ( B C ) ¯ = [ by prop. (2) ] = A ( B C ) .
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