Need typed solution only

5. Show that -p - (q - ") and q - (pVr) are logically equivalent, in two different ways: (i) use a truth table, (ii) without using truth tables. 6. Show that (pAq) - r and (p - r)A (q -+ r) are not logically equivalent, without using truth tables. 7. Express each of these statements into logical expressions using predicates, quantifiers, and logical connectives. Let the domain consist of all people. Let S(x) be "r is in your class," P(x) be "r is perfect." (a) Nobody is perfect. (Use only the universal quantifier.) (b) Nobody is perfect. (Use only the existential quantifier.) (c) Nobody in your class is perfect. (d) Not everybody is perfect. (e) Someone in your class is perfect. (f) Not everyone in your class is not perfect. 8. In the previous problem, put a negation in front of the logical expression for "Someone in your class is perfect", then move the negation until negation only appears directly in front of S(x) or P(x), by applying DeMorgan's Laws