solve and answer the following handwritten only neat and clean

1. Write each statement in words. Let p: The plane is on time. Let q: The sky is clear. (a) PA (-q) (b) q - (pv-p) (c) p + q 2. Construct a truth table for each proposition. (a) [(p/q) vr] + [(pAr )v(qar)] (b) [(PAr) - (9A -)] - [(p/q) vr)] 3. Prove the De Morgan's Laws by constructing truth tables. 4. Let % := Letters in the English Alphabet = {a, b, c, .. . ,x, y, 2} A = {t, r, i, a, n, g, l, e, s} B = {s, q, u, a, r, e }, C = {h, e, x, a, g, o, n, s } Determine the following: (a) AU(Bnic) (b) (AUBY'nc (c) (Anc)U (Bnc) (d) An(Cn* )' (e) n[(AUB)n (BUC)] 5. A survey of 90 customers was taken at Barnes & Noble regarding the types of books purchased. The survey found that 44 purchased mysteries, 33 purchased science fiction, 29 purchased romance novels, 13 purchased mysteries and science fiction, 5 purchased science fiction and romance novels, 11 purchased mysteries and romance novels, and 2 purchased all three types of books (mysteries, science fiction, romance novels). How many of the customers surveyed purchased (a) mysteries only? (b) mysteries and science fiction, but not romance novels? (c) mysteries or science fiction? (d) romance novels or mysteries, but not science fiction? (e) exactly two types (mysteries, science fiction, romance novels)