Complete the following exercises for combinational logic design and show your work. (a) Complete a truth table that has 3 inputs (A, B, and C) and one output (F). F is asserted (1) whenever both B and C are deasserted (0). F is asserted (1) whenever A is deasserted (0). F is deasserted (0) in all other cases. (b) Determine the sum-of-products equation for F. Show the terms instead of the minterm abbre- viations (show ABC instead of m7). (c) Determine the product-of-sums equation for F. Show the terms instead of the maxterm abbre- viations (show A+B+C instead of M7). (d) Prove that F from question b is equivalent to F = A + BC using proof by rewrite. HINT: remember the uniting law is the key to minimization. (e) Draw the gate diagram for F = A + BC.