Simplify boolean expression $AB + A\bar B+ ABC $

Question

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.

So $(AB)' = \overline{AB}$ which means the complement of $AB$? What does + mean here? xor? — Henno Brandsma, Nov 14 '15 at 14:54
Sorry i posted the wrong question. Check below comment or updated version. — GNov, Nov 14 '15 at 14:55
I think it is xor. The assignment is just says Simplify, using the laws of Boolean algebra: AB + AB̅+ ABC — GNov, Nov 14 '15 at 14:56
What are your 10 laws that you are allowed to use? reference? — Henno Brandsma, Nov 14 '15 at 15:15

score 0 · Accepted Answer · answered Nov 14 '15 at 15:01

0

$AB + A\overline{B} + ABC = A(B + \overline{B}) + ABC = A + ABC = A(1 + BC) = A\overline{BC}$

answered Nov 14 '15 at 15:01

Henno Brandsma

Can't you simply replace $1+BC$ with $1$ (so that the final result is $A$)? – barak manos Nov 14 '15 at 15:07
Not if + means xor, which was my assumption. Then $1+X$ is 0 if $X$ is 1, and vice versa. So $1+X = \overline{X}$. – Henno Brandsma Nov 14 '15 at 15:08
Yeah, I just read the comments to the question. Since when is "$+$" = XOR? I'd expect it to be OR. – barak manos Nov 14 '15 at 15:09
It's common in Boolean functions. – Henno Brandsma Nov 14 '15 at 15:09
Isn't that the plus with a circle around it? – barak manos Nov 14 '15 at 15:10
You can see BA as having basic operations $\lor,\land,\lnot$ or $+,\cdot,'$ axiomatically. Boolean rings etc. A Boolean ring is just a commutative unitary ring $R$ with $x + x = 0$ for all $x$. A BA is then defined by $\lnot x = 1 + x$, $x \lor y = x + y + xy$, $x \land y = xy$. It's a common different view. Yes, sometimes $x \oplus y$ is also used, in CS contexts. – Henno Brandsma Nov 14 '15 at 15:11
I have done the translate in Italian language and your last answer it is perfect! – Sebastiano Aug 22 '20 at 15:32

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