1. No woman is both a politician and a housewife. Write this sentence in symbolic form. 2. If A = {∅, {∅}} and B = {∅}, then find A − B. 3. If the truth value of p ∨ q is false, then compute the truth value of ((¬p ∨ q) ∧ r) ⇔ (r ⇒ (p ∧ q)). 4. Let A = {3, 5} and B = {−2, 2}. What is the the truth value of (∃x ∈ A)(∀y ∈ B)(x = y2 − 1)? 5. Find the negation of (∀x)(∃y)(y < x − 3). 6. Let An = {x | x ∈ Z ∧ 0 < x ≤ n}, where n ∈ N . Then compute (a) A7 \ S 5 n =2 An = (b) T 8 n =3 An = 7. Determine whether or not each of the following argument is valid or not. (a) ¬p ∧ q, r ⇒ p, ¬r ⇒ s, s ⇒ t |= t (b) If the moon is made of babanas, then there are monkeys on the moon. The moon is not made of babanas. Threfore, there are no monkeys on the moon. 8. In a movie house, 24 people like animated film, 16 people like dramatic films, 8 people like comedy films, 5 people like both animated and comedy films, 8 people like comedy and drama, 12 people like animated and drama and 3 people like all the three types. How many people like (a) only comedy and drama? (b) only dramatic and animated?​