Logic Gates

The given expression is .

Step 1: Simplify
First, expand :

Step 2: Simplify
Next, observe that , so we can rewrite the second part: Now expand:

Step 3: Combine both parts
Now, combine the two parts of the expression: Simplifying this:

Step 4: Factor the expression
The final simplified expression is: Thus, the answer is .

In a logic circuit with inputs A, B, and C, each input can take values 0 or 1. Since there are three binary inputs, the total number of input combinations is:

We are interested in the number of combinations that result in output .

From the logic of the circuit, the combinations that result in are:

1. , ,
2. , ,
3. , ,
4. , ,
5. , ,
6. , ,
7. , ,

So, the number of combinations giving output is 7.

Correct option: (C): 7