4. [12 marks] Rewrite cach of the following theorems using quantifiers and predicates. Note that the theorems are not precisely stated. It is up to you to choose reasonable sets from which the variables should be drawn. Further, notice that the definitions we have given you should be stated as predicates, but we would like you to formalize their specification. Make sure that your theorems have no unbound variables. You are not allowed to use predicates Even or Odd, but you can use a predicate Prime) that is True if r is a prime, and False otherwise. a. [4 marks] Goldbach Conjecture: Every even integer greater than 2 can be written as the sum of two primes. b. [4 marks] The product of a rational number r by an irrational number is rational if and only if I=0. c. (4 marks] The sum of two odd integers is an even integer. 4. [12 marks] Rewrite cach of the following theorems using quantifiers and predicates. Note that the theorems are not precisely stated. It is up to you to choose reasonable sets from which the variables should be drawn. Further, notice that the definitions we have given you should be stated as predicates, but we would like you to formalize their specification. Make sure that your theorems have no unbound variables. You are not allowed to use predicates Even or Odd, but you can use a predicate Prime) that is True if r is a prime, and False otherwise. a. [4 marks] Goldbach Conjecture: Every even integer greater than 2 can be written as the sum of two primes. b. [4 marks] The product of a rational number r by an irrational number is rational if and only if I=0. c. (4 marks] The sum of two odd integers is an even integer