The Boolean function for shown in the F table below is most nearly:

A	B	C	F
0	0	0	1
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	1
1	0	1	1
1	1	0	0
1	1	1	0

A.  $$barA+barB$$
B.  $$barBbarAbarC$$
C.  $$B+barAbarC$$
D.  $$barB+barAbarC$$

To create a Boolean function from a truth table, we combine all of the expressions that output a value of F = 1. Since F= 1 is true 5 separate times, we'll start off with 5 expressions:

$F = A\text{'}B\text{'}C\text{'} + A\text{'}B\text{'}C + A\text{'}BC\text{'} + AB\text{'}C\text{'} + AB\text{'}C$

This is the base of our expression. Now, we are interested in applying theorems in order to simplify the Boolean expression in its most basic form.

First, if we take a look at our equations, it becomes clear that B' is present across 4 of them. In other words, for every combination of A, A', C, and C', if B' is present, the expression F will automatically be true. Factoring out the B' and applying the compliment rule:

$$\begin{gathered} Compliment Rule: A+\overline{A} = 1 \\ F = (A\text{'}B\text{'}C\text{'} + A\text{'}B\text{'}C + AB\text{'}C\text{'} + AB\text{'}C) + A\text{'}BC\text{'} \\ F = B\text{'}(A\text{'}C\text{'} + A\text{'}C + AC\text{'} + AC) + A\text{'}BC\text{'} \\ F = B\text{'} +A\text{'}BC\text{'} \end{gathered}$$

We can then apply the absorption law to simplify our answer further:

$Absorption Law: AB+\overline{A} = B+\overline{A}$

$$\begin{gathered} F = B\text{'} +A\text{'}BC\text{'} \\ F = B\text{'} + A\text{'}C\text{'} \end{gathered}$$

This is the most simplified form of our Boolean expression. Therefore, our answer here is D.