(programming required) Consider the class of circuits from Exercises 3.84–3.87: inputs {p, q,r}, and at most three gates chosen from {∧,∨, ¬}. There are a total of 28 = 256 distinct propositions over...

(programming required) Consider the class of circuits from Exercises 3.84–3.87: inputs {p, q,r}, and at most three gates chosen from {∧,∨, ¬}. There are a total of 28 = 256 distinct propositions over inputs {p, q,r}: eight different input configurations, each of which can turn the light on or leave it off. Write a program to determine how many of these 256 propositions can be represented by a circuit of this type. (If you design it well, your program will let you check your answers to Exercises 3.84–3.88.)

Exercises 3.84–3.87

The light is on when the true inputs are {q} or {r}. The light is off when the true inputs are {p} or {p, q} or {p, q,r}

The light is off when the true inputs are {p, q} or {p,r} or {q,r} or {p, q,r}