Design a 3-input logic circuit that performs the function F = (X + Y) Z’. Draw the circuit diagram and truth table.

The Boolean function is given as:

F=(X+Y)Z′

To design the circuit:

• The inputs X and Y are first OR-ed together, so an OR gate is used to perform X+Y.
• The input Z is inverted using a NOT gate, so we get Z′.
• Finally, the output of the OR gate and the NOT gate are AND-ed together using an AND gate to give the final output F.

Circuit diagram:

• Inputs X and Y go to an OR gate.
• Input Z goes to a NOT gate.
• The output of the OR gate and the NOT gate goes to an AND gate.

Truth table:

The circuit implements the required function by performing an OR operation between X and Y, inverting Z, and then performing an AND operation to combine them.