Question

given that the input a is false and the input c is false, how would the value of input b affect the final output?
answer
the output will be true no matter what the value of input b is.
the output will be false no matter what the value of input b is.
if b is true then output will be true. if b is false then output will be false.
if b is true then output will be false. if b is false then output will be true.

Explanation:

Step1: Evaluate NOT C

Given $C = \text{false}$, $\text{NOT } C = \text{true}$

Step2: Test B = true case

1. Evaluate NOT B: $\text{NOT } \text{true} = \text{false}$
2. Evaluate A OR NOT B: $\text{false} \lor \text{false} = \text{false}$
3. Evaluate NOT (A OR NOT B): $\text{NOT } \text{false} = \text{true}$
4. Evaluate final AND: $\text{true} \land \text{true} = \text{true}$

Step3: Test B = false case

1. Evaluate NOT B: $\text{NOT } \text{false} = \text{true}$
2. Evaluate A OR NOT B: $\text{false} \lor \text{true} = \text{true}$
3. Evaluate NOT (A OR NOT B): $\text{NOT } \text{true} = \text{false}$
4. Evaluate final AND: $\text{false} \land \text{true} = \text{false}$

Answer:

If B is true then output will be true. If B is false then output will be false.