4. Construct a circuit using inverters, OR gates, and AND gates that gives an output of 1 if three people on acommittee do not all vote the same.

The Boolean expression for the output of the circuit is:

f(a, b, c) = (a ∧ ¬b ∧ ¬c) ∨ (¬a ∧ b ∧ ¬c) ∨ (¬a ∧ ¬b ∧ c)

where ∧ represents the logical AND operator, ∨ represents the logical OR operator, and ¬ represents the logical NOT operator.

To construct the circuit using inverters, OR gates, and AND gates, we can first use inverters to obtain the negation of each input variable:

¬a, ¬b, ¬c

Next, we can use AND gates to obtain the product terms in the Boolean expression:

a ∧ ¬b ∧ ¬c, ¬a ∧ b ∧ ¬c, ¬a ∧ ¬b ∧ c

Finally, we can use OR gates to obtain the sum of the product terms, which gives the final output of the circuit:

f(a, b, c) = (a ∧ ¬b ∧ ¬c) OR (¬a ∧ b ∧ ¬c) OR (¬a ∧ ¬b ∧ c)

The circuit diagram is shown below:

     ____      ____      ____
a ---|    |----|    |----|    |---- f
    | AND|    | OR |    |    |
b ---|____|    |____|----|    |
                        | AND|
c ----------------------|____|

In the circuit diagram, each AND gate represents one of the product terms, and the OR gate represents the sum of the product terms. The output of the circuit is connected to the f node, which gives an output of 1 if three people on a committee do not all vote the same.