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I would like help simplifying this boolean algebra expression:

B*C + ~A*~B + ~A*~C => A*B*C + ~A

I need to know the steps of how to simplify it to the ABC + ~A

'*' indicates "AND"

'+' indicates "OR"

"~A" indicates "A NOT"

Any help would be appreciated! Thank you!

Paigentry
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1 Answers1

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For a better view, i'll skip * for conjunction, and use ' for negation.

First you shall expand the 2 term disjunctions: Expand B*C , A'*B' and A'*C'

1) (A + A')BC + A'B'(C + C') + A'(B + B')C'

now distribute the parentheses.

2) ABC + A'BC + A'B'C + A'B'C' + A'BC' + A'B'C'

the fourth term and the last term are the same, A'B'C', so ignore one of them since p + p = p or you can expand the situation for your needs (might be needed for some situations) as in p+p+p+p+....+p = p

3) So now, lets try to search for common terms. See the 2nd term and 5th term, A'BC and A'BC'. Take common parenthesis, A'B(C+C') => A'B. Do the same for 3rd term and the 4th term, A'B'C and A'B'C'. A'B'(C+C') => A'B' since X+X' = 1.

now we have:

ABC + A'B + A'B'

4) take common parenthesis again, 2nd and 3rd term: A'(B+B')

There you have ABC + A'

BC + A'B' + A'C' => ABC + A'

Varaquilex
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