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 Algebra Pre-Algebra and Basic Algebra Math Forum

 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. Tags algebra, boolean, help or question Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post JustForFun2000 Computer Science 2 September 26th, 2016 09:11 AM unistu Algebra 4 March 27th, 2016 09:54 PM topsquark Abstract Algebra 5 September 12th, 2014 03:48 PM sailorman444 Algebra 1 January 9th, 2014 07:21 AM MoZ Applied Math 8 January 28th, 2009 05:29 PM

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