Exercise 6. Using the the proposition laws (not the truth tables) prove that (?)^q) ? (?(q ? p)) is tautology IIO Exercise 7. Symbolize the following by using quantifiers, predicates, and logical operators(connectives a) The square of any real number is greater than or equal to zero. b) Some integers are multiples of 7. c) There is a unique natural number such that 22-16 d) For each integer, there exists an integer such that their sum is 0. Exercise 8. In this exercise, the predicate P() denotes r is an odd integer and Q(r) denotes r is a prime integer, and R(r) is 22 is an odd integer. Write a statement in English corresponding to cach symbolic statement. a) Vr(P(z) ? R(z)) b) V2(P(z)/\ Q(z)) c) 3x(P(x)^ Q(z))