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September 13th, 2018, 08:32 AM  #1 
Newbie Joined: Sep 2018 From: Europe Posts: 2 Thanks: 0  Boolean algebra help/question
Hi guys, I have been asked to solve this question > AB + A'C + BC, the answer to the question is > AB + A'C + BC = AB + A'C + BC(A + A') = AB + A'C + ABC + A'BC = AB + ABC + A'C + A'BC = AB(1 + C) + A'C(1 + B) = AB + A'C . Where did the (A + A') come from? Here is another example: (A + C) (A + B + C), so first I will multiply both brackets and I get AA + AB + AC + CA + CB + CC. AA = A and CC = C, so now I'm left with A + AB + AC + CA + CB + C, A and AB have A in common, so A(B + 1) = A now I'm left with A + AC + CA + CB + C, A and AC both have A in common, so A(C + 1) = A. Now I'm left with A + CA + CB + C, I will rearrange the variables A + C + CA + CB, C and CA both have C in common, so C(A + 1) = C. Now I'm left with A + C + CB . C and CB both have C in common, so C( B + 1) = C, so the final answer is A + C. I checked a few trusted online boolean algebra calculators and indeed this is the correct answer. I also tried this method on many other questions and got the correct answer, but how is AB + A'C + BC any different?? How I solved it, I did AB + BC + A'C. AB and BC both have B in common, so B(A + C + 1) = B. The reason why I did + 1 is because there is an implicit one after AB right? I then got B + AC', I must have gone wrong somewhere? Thanks. Last edited by skipjack; September 13th, 2018 at 11:38 AM. 
September 14th, 2018, 03:23 AM  #2 
Senior Member Joined: Apr 2014 From: UK Posts: 898 Thanks: 329 
(A+A') is just 1, so BC is the same as BC(A+A') In your second example, you didn't quite show the correct working: After multiplying out: AA + AB + AC + CA + CB + CC A(1+B+C) + C(A+B+1) A + C You missed one of the terms in each bracket which made it less obvious what you were doing. AB + BC is not the same as B(A + C + 1), that would imply BA + BC + B, well, there isn't a B. The implicit 1 you appear to have added is AB = B(A+1) instead of BA1. 
September 14th, 2018, 07:28 AM  #3 
Newbie Joined: Sep 2018 From: Europe Posts: 2 Thanks: 0 
Thanks Dave but let's say we have A + AC It equals A(C + 1) why is this? where does this 1 come from? Does the one from from C or does it come from A? And if you have AB + BC why wouldn't it be B(A + C + 1 ) because in the above example it was C + 1? Why doesn't the 1 apply here? Thanks. Last edited by skipjack; September 22nd, 2018 at 01:16 PM. 

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