# Math Help - Boolean Expression

1. ## Boolean Expression

Hello,

Ok so I have the following equation: A'B'C + A'BC + AB'C + ABC' + ABC

I know that the most simplified form is AB + C but I cannot arrive at that solution.
Every time I try to work it out the first thing I do is Simplify the last two terms as follows: AB(C' + C) = AB

So the new equation is: A'B'C + A'BC + AB'C + AB

Now I tried removing C and getting the following: C(A'B' + A'B + AB') + AB

From here I am stuck and I have tried to solve it many other ways but always get stuck or eliminate something I don't want to. Help would be much appreciated

2. A'B'C + A'BC + AB'C + ABC' + ABC

= A'B'C + A'BC + AB'C + ABC + ABC'
= C + ABC'
Let AB = X, then we have
C + XC'
= C(X+X') + XC'
= C(X + X' + X) + XC'
= C(X + X') + X(C+C')
= C + X
= C + AB

3. The problem is that the expression by which C is multiplied, i.e., A'B' + A'B + AB' is not a tautology. We can turn it into one by adding a second copy of ABC to the original expression. The expression is then broken into two parts: ABC + ABC' = AB and A'B'C + A'BC + AB'C + ABC = C(A'B' + A'B + AB' + AB) = C.

By the way, the original formula is not an equation; an equation must have an = sign.