The logic circuit for the Boolean expression F = A + B + C is shown below.

``` A B C F ---------------- 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 ```

The circuit consists of three AND gates and one OR gate. The AND gates are used to combine the inputs A, B, and C. The OR gate is used to combine the outputs of the AND gates.

The operation of the circuit can be understood by following the truth table. For example, when A = 0, B = 0, and C = 0, the output of the first AND gate is 0, the output of the second AND gate is 0, and the output of the third AND gate is 0. The output of the OR gate is also 0.

When A = 0, B = 0, and C = 1, the output of the first AND gate is 0, the output of the second AND gate is 1, and the output of the third AND gate is 1. The output of the OR gate is also 1.

The logic circuit for the Boolean expression F = A + B + C can be used to implement a variety of logical operations. For example, the circuit can be used to implement a half-adder, a full-adder, or a multiplexer.

The logic circuit for the Boolean expression F = A + B + C is a simple example of how logic gates can be used to implement complex logical operations.

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