Simplifying Expressions with Boolean Algebra - Homework Help

[EEhokie13]

Homework Statement

Simplify the following expressions using Boolean Algebra.

a) A + AB (A or A and B)
b) A'BC + AC (A(not) and B and C or A and C)
c) A'B + ABC' + ABC (A(not) and B or A and B and C(not) or A and B and C)

Homework Equations

Some simple boolean algebra rules.
x+1=0
x*x=x
x*x'=0

The Attempt at a Solution

For a, I got the answer of A.
I did:
A(1 + B)
A(1)
= A

For b, I got the answer AC.

I did:
C(A'B + A)
C(0 + A)
= AC

For c, I got the answer AB.
I did:
B(A' + AC' + AC)
B(A' + (A.C') + (A.C))
B(A' + (0) + A)
B(A' + A)
B(A)
= AB

Are my calculations correct or am I completely wrong? Thank you for your help.

 

[vela]

Homework Statement

Simplify the following expressions using Boolean Algebra.

a) A + AB (A or A and B)
b) A'BC + AC (A(not) and B and C or A and C)
c) A'B + ABC' + ABC (A(not) and B or A and B and C(not) or A and B and C)

Homework Equations

Some simple boolean algebra rules.
x+1=0
x*x=x
x*x'=0

The Attempt at a Solution

For a, I got the answer of A.
I did:
A(1 + B)
A(1)
= A

Looks good.

For b, I got the answer AC.

I did:
C(A'B + A)
C(0 + A)
= AC

How did you replace A'B with 0?

For c, I got the answer AB.
I did:
B(A' + AC' + AC)
B(A' + (A.C') + (A.C))
B(A' + (0) + A)
B(A' + A)
B(A)
= AB

It's not clear what you did from the second to third line, and you simplified A'+A incorrectly.

Are my calculations correct or am I completely wrong? Thank you for your help.

When you have only a few variables, it's easy enough to verify that you simplified an expression correctly by writing out the truth table. For example, for A'BC+AC, you get

A B C   A'  A'BC   AC    A'BC+AC
T T T   F     F     T       T
T T F   F     F     F       F
T F T   F     F     T       T
T F F   F     F     F       F 
F T T   T     T     F       T
F T F   T     F     F       F
F F T   T     F     F       F
F F F   T     F     F       F

Comparing the columns for AC and A'BC+AC, you can see they're not equal, so you know something went wrong in the simplification.