Simplify $AB + A\bar B+ ABC $
I've been trying to simplify for a good while now. I'm using only the 10 rules but cannot find a way to simplify fully.
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$\begingroup$ So $(AB)' = \overline{AB}$ which means the complement of $AB$? What does + mean here? xor? $\endgroup$– Henno BrandsmaNov 14, 2015 at 14:54
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$\begingroup$ Sorry i posted the wrong question. Check below comment or updated version. $\endgroup$– GNovNov 14, 2015 at 14:55
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$\begingroup$ I think it is xor. The assignment is just says Simplify, using the laws of Boolean algebra: AB + AB̅+ ABC $\endgroup$– GNovNov 14, 2015 at 14:56
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$\begingroup$ What are your 10 laws that you are allowed to use? reference? $\endgroup$– Henno BrandsmaNov 14, 2015 at 15:15
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1 Answer
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$AB + A\overline{B} + ABC = A(B + \overline{B}) + ABC = A + ABC = A(1 + BC) = A\overline{BC}$
answered Nov 14, 2015 at 15:01
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$\begingroup$ Can't you simply replace $1+BC$ with $1$ (so that the final result is $A$)? $\endgroup$ Nov 14, 2015 at 15:07
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$\begingroup$ Not if + means xor, which was my assumption. Then $1+X$ is 0 if $X$ is 1, and vice versa. So $1+X = \overline{X}$. $\endgroup$ Nov 14, 2015 at 15:08
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$\begingroup$ Yeah, I just read the comments to the question. Since when is "$+$" = XOR? I'd expect it to be OR. $\endgroup$ Nov 14, 2015 at 15:09
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$\begingroup$ Isn't that the plus with a circle around it? $\endgroup$ Nov 14, 2015 at 15:10