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I wanna ask some basic law of boolean algebra. What i learn is :

 1. A+A'B=A+B
 2. A+AB'=A+B'
 3. A+AB=A
 4. A+A'B'=A+B'

but i meet some condition like : A'+AB

so, what is the answer for A'+AB?

codingEnthusiast
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Hollow Looi
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  • I'm voting to close this question as off-topic because it is about algebra, not programming. – Pang Apr 27 '15 at 02:59

2 Answers2

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Let's say A' = D so when A is false, then D is true and vice versa.

Then A' + AB = D + D'B and if you understand your first equation:

D + D'B = D + B = A' + B

Regarding your comment:

I'll use this equality: AB + A'B = B and I will combine the first with the third and the second with the fifth term:

x'y'z'+x'yz+xy'z'+xy'z+xyz = y'z' + yz + xy'z

Now, from the result, I can do this:

y'z' + yz + xy'z = yz + y'(z' + zx)

and now, using using A' + AB = A' + B:

yz + y'(z' + zx) = yz + y'(z' + x) = yz + y'z' + y'x

or do this:

y'z' + yz + xy'z = y'z' + z(y+ xy') = y'z' + z(y + x) = y'z' + zy + xz

Are they different? No, take a look at this:

x y z | yz + y'z' + y'x | y'z' + zy + xz
0 0 0 |       1         |       1
0 0 1 |       0         |       0
0 1 0 |       0         |       0
0 1 1 |       1         |       1
1 0 0 |       1         |       1
1 0 1 |       1         |       1
1 1 0 |       0         |       0
1 1 1 |       1         |       1
codingEnthusiast
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  • i m currently doing x'y'z'+x'yz+xy'z'+xy'z+xyz...the answer i get is y'x+y'z'+yx+yz. Is it my answer right or wrong? if wrong can show me the real answer with step please? – Hollow Looi Apr 26 '15 at 19:08
  • the question is f=x'y'z'+x'yz+xy'z'+xy'z+xyz the answer i get is y'x+y'z'+yx+yz. I wanna to know the real answer for f. Its is combinational circuit functional behavior-synthesis. – Hollow Looi Apr 26 '15 at 19:19
  • I have provided this in my answer, see above please. – codingEnthusiast Apr 26 '15 at 19:27
  • ohya.i miss read it. Thanks dude , but i not understand about the equality.... The equality is choosing which have the same term right?but sometime i choose the different one...For example i choose 3rd and 4rd which is same y' term. This move is wrong? EDIT: Why the answer show in my answer sheet about this question is y'z'+yz+xz ? – Hollow Looi Apr 26 '15 at 19:33
  • I have edited my answer and fixed a mistake, I have also provided two results which are identical. `yz + y'z' + y'x` and `y'z' + zy + xz` might seem different at first but if you do the logic tables for these you ll see they are equal. – codingEnthusiast Apr 26 '15 at 19:52
  • You can choose different ways to solve the problem, which will yield different results, there's no problem with that, because the function that you will end up to will be identical. – codingEnthusiast Apr 26 '15 at 19:53
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You can use this open source project to solve basic boolean expression, its solve all the basic boolean expression

Ibukun Muyide
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