# Simplify Sum of Products: $\;A'B'C' + A'B'C + ABC'$ [closed]

How would you simplify the following sum of products expression using algebraic manipulations in boolean algebra?

$$A'B'C' + A'B'C + ABC'$$

## closed as off-topic by Jack, Stefan4024, kimchi lover, Rebellos, LeucippusDec 10 '17 at 2:13

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• You have to say a bit about what each letter represents. Matrices? – rcorty Nov 20 '13 at 15:37
• Its boolean algebra – user550 Nov 20 '13 at 15:38
• wolframalpha.com/input/… – user550 Nov 20 '13 at 15:50

Essentially, all that's involved here is using the distributive law (DL), once.

Distributive Law, multiplication over addition: $$PQ + PR = P(Q + R)\tag{DL}$$

In your expression, in the first two terms, put $P = A'B'$:

We also use the identity $$\;P + P' = 1\tag{+ID}$$

\begin{align} A'B'C' + A'B'C + ABC' & = A'B'(C' + C) + ABC' \tag{DL}\\ \\ &= A'B'(1) + ABC' \tag{+ ID}\\ \\ & = A'B' + ABC'\end{align}

Hint: the first two terms are the same except for the $C'$ or $C$. Put those two terms together.

• So A'B' + ABC' ? – user550 Nov 20 '13 at 15:44