1. Express the following English sentences as propositions in predicate logic. Then give the negation of the proposition you have given in predicate logic and as an English sentence (a) The Goldbach conjecture: Every even integer greater than 2 can written as the sum of two prime numbers. (Recall that a number p is prime if p > 1 and the only factors that p has are itself and 1. You may use a predicate such as P(n) n is prime.) (b) There is a largest real number. (c) Any two sets have an intersection. (d) There is a set that contains every element and has every set as a subset 1. Express the following English sentences as propositions in predicate logic. Then give the negation of the proposition you have given in predicate logic and as an English sentence (a) The Goldbach conjecture: Every even integer greater than 2 can written as the sum of two prime numbers. (Recall that a number p is prime if p > 1 and the only factors that p has are itself and 1. You may use a predicate such as P(n) n is prime.) (b) There is a largest real number. (c) Any two sets have an intersection. (d) There is a set that contains every element and has every set as a subset