Boolean Equation Expression

dukeofsmooth

Joined Feb 5, 2009
2
Can someone please simplify the Boolean expression-
AB'C + A'BC + A'B'C

I worked the this expression in the following way...
C(A'B + A'B' + AB')
C[ A' (B + B') + AB']
C[ A' (1) + AB']
C(A' + AB')
A'C + AB'C

The text book answer is A'C + B'C

Thank you,
Jesse

Last edited:

Ratch

Joined Mar 20, 2007
1,068
Hi there, Duke of Suave,

Can someone please simplify the Boolean expression-
AB'C + A'BC + A'B'C
Let's do your prob another way.

C(A'B + A'B' + AB')
C(A'B + A'B'+ A'B' + AB')
C(A'(B + B') + (A' + A)B')
C(A' + B')
A'C + B'C and the answer book is correct.

Or another way to solve it: your second to the last expression contains: A' + AB' .

The dual is A'(A + B') which easily reduces to A'B' .

Taking the dual again and multiplying by C gives C(A' + B') = A'C + B'C