Minimum number of gates required to implement the boolean function ab c using only 2-input NOR gates:

To determine the minimum number of 2-input NOR gates required to implement the boolean function ab c, we need to analyze the function and find the most efficient way to express it using NOR gates.

Understanding the boolean function:
The boolean function ab c takes three inputs: a, b, and c. It returns true (1) if both a and b are true (1), and false (0) otherwise. The output is then combined with c using the logical OR operation.

Step-by-step approach:
To implement the boolean function using NOR gates, we can follow these steps:

1. Implement the AND gate using NOR gates:
- The AND gate returns true (1) if both of its inputs are true (1), and false (0) otherwise.
- To implement an AND gate using NOR gates, we can connect two NOR gates in series, with their outputs connected to the input of a third NOR gate.
- The inputs of the two NOR gates are the complement of the original inputs.
- The output of the third NOR gate will be the result of the AND operation.

2. Implement the OR gate using NOR gates:
- The OR gate returns true (1) if at least one of its inputs is true (1), and false (0) otherwise.
- To implement an OR gate using NOR gates, we can connect two NOR gates in parallel, with their outputs connected to the input of a third NOR gate.
- The inputs of the two NOR gates are the original inputs.
- The output of the third NOR gate will be the result of the OR operation.

3. Combine the AND and OR gates:
- The output of the AND gate will be the result of the logical AND operation between a and b.
- The output of the OR gate will be the result of the logical OR operation between the output of the AND gate and c.

Calculating the minimum number of gates:
Using the above approach, we can implement the boolean function ab c using a minimum of three 2-input NOR gates:

- Two NOR gates connected in series to implement the AND gate.
- One NOR gate connected in parallel with the AND gate to implement the OR gate.

Conclusion:
In conclusion, the minimum number of 2-input NOR gates required to implement the boolean function ab c is three. This can be achieved by implementing an AND gate using two NOR gates connected in series, and an OR gate using two NOR gates connected in parallel with the AND gate.