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, \( \text{OR}(A, B) \) is true if at least one input is true. Since A is true, \( \text{OR}(A, B) = \text{true} \) (regardless of B's value).

Step2: Analyze AND Gate Output

The AND gate takes inputs C (true) and the output of the OR gate (true). For an AND gate, \( \text{AND}(C, \text{OR}(A,B)) \) is true only if both inputs are true. Since C is true and OR output is true, \( \text{AND}(C, \text{OR}(A,B)) = \text{true} \), no matter B's value.

Answer:

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