Simplify Sum of Products: $\;A'B'C' + A'B'C + ABC'$

Question

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

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

Answer 1

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 $$\;P + P' = 1\tag{+ID}$$

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

Answer 2

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