1. Simplify the following Boolean expressions to expressions containing a mini-mum number of literals [Proof of work is must] a) (X + Y)(X + Y) b) (PQR + PQ + PQ R)

2. Prove the following Boolean expressions [Proof of work is must] a) A C + ABC + A C = AB + C b) KL MN + KLN + KLMN = LN

5. Optimize the following Boolean functions by means of a 3-variable K-map [Proof of work is must] a) F(A, B, C) = m(0, 2, 4, 5, 6) + dc(7) a) F(L, M, N) = m(1, 2, 3, 7) c) F(W, X, Y) = M(0, 4, 5, 6) dc(7) d) F(P, Q, R) = M(2, 3, 4, 6)