1. Give an example of a truth table requiring between 3 billion and 5 billion rows that can be constructed using fewer than 40 (but at least 1) two-input gates.
2. Give an example of a circuit with a cyclic path that is nevertheless combinational.
3. Alyssa P. Hacker says that any Boolean function can be written in minimal sum-of-products form as the sum of all of the prime implicants of the function. Ben Bitdiddle says that there are some functions whose minimal equation does not involve all of the prime implicants. Explain why Alyssa is right or provide a counterexample demonstrating Ben's point.