Question

the diagram below shows a circuit composed of two logic gates labeled or and and. each gate takes two inputs and produces a single output.
if the inputs a and c are both true which of the following best describes the output of the and gate?
a the output will be true no matter what the value of input b is.
b the output will be false no matter what the value of input b is.
c the output will be true if input b is true; otherwise it will be false.
d the output will be false if input b is true; otherwise it will be true.

Explanation:

Step1: Analyze OR Gate Output

The OR gate takes inputs A and B. Given A is true. For an OR gate, if at least one input is true, the output is true. So OR output = \( A \lor B \). Since \( A = \text{true} \), \( A \lor B = \text{true} \) (regardless of B).

Step2: Analyze AND Gate Output

The AND gate takes inputs (OR output) and C. C is true, and OR output is true (from Step1). For an AND gate, output is true only if both inputs are true. So AND output = \( (\text{OR output}) \land C \). Since both are true, output is true, no matter B.

Answer:

A. The output will be true no matter what the value of input B is.