Problem 2 (Proving theorems!) [20 marks] For each of the following statements, translate it into predicate logic and prove it, if the statement is true, or disprove it, otherwise: 1. for any two even integers, there exists a third integer (even or odd the double of which is equal to the sum of the first two integers. 2. for any two odd integers, there exists a third integer (even or odd) the triple of which is equal to the sum of the first two integers