hi there ,
can you please help to prove these Boolean Algebra expression :

(A+B) (A`+C) = AC+A`B

and

AB+A`C = (A+C)(A`+B)

 

Take a moment to review the material on Boolean Algebra contained in the AAC ebook. I think you will find it a good supplement to any information in your course textbook.

hgmjr

 

Both problems are the same. So when you solve the first one, the second one is done.

 

Try laying out a truth table for each, this will constitute a proof.

 

I know how to prove it using truth table but I need to prove it mathematically

can you help me in this ?

 

I know how to prove it using truth table but I need to prove it mathematically

can you help me in this ?

Do you know how to multiply out the left hand side of the first equation?

If you multiply it out, you will have 4 terms. Two of these terms will match the right hand side. Can you figure out why the extra two terms are redundant and not necessary?

 

just-gal,

I know how to prove it using truth table but I need to prove it mathematically

can you help me in this ?

Yes, I can.

(A+B)(A'+C) = AC+A'B                     ; equation to be proved
(A+B)(A'+C) = AA'+AC+A'B+BC = AC+A'B+BC  ; AA' = 0
A(B+B')C+A'B)(C+C')+(A+A')BC             ; (X+X') = 1
ABC+AB'C+A'BC+A'BC'+ABC+A'BC             ; expand expression
ABC+AB'C+A'BC+A'BC'                      ; eliminate redundant terms
AC(B+B')+A'B(C+C') = AC +A'B             ; factor out (X+X')

Therefore the Boolean equation has been proven correct.

AB+A'C is the dual of the left side of the original equation (A+B) (A'+C). and (A+C)(A'+B) is the dual of the right side of the original equation AC+A'B. Therefore, AB+A'C = (A+C)(A'+B) because the two expressions are duals of an Boolean equation that was proven correct.

Ratch

 

Does this list of standard Boolean results help?

0.0 = 0
0+0 = 0

1.1 = 1
1+1 = 1

1.0 = 0
1+0 = 1

0'= 1
1'= 0

A+0 = A
A+1 = 1
A.0 = 0

A.1 = A
A+A =A
A.A = A
A+A' = 1
A.A' = 0
(A')' = A

A+A.B = A
A.(A+B) = A
A.(A'+B) = A.B
A+A'.B = A+B

A+B.C = (A+B).(A+C)

(A.B)'= A'+B'

A'.B' = (A+B)'

 

That's really helped me soo much , thank you soo much

 

holy crap! I hope that one day I will understand a single word of this thread.

 

mango matto,

holy crap! I hope that one day I will understand a single word of this thread.

There are no advanced concepts covered in this thread. Everything is basic logic principles covered in any good textbook or course in digital logic. This knowledge is readily available from several sources. All you have to do is read and understand. If one source does not explain it to your satisfaction, try another.

Ratch