Please prove it and translate it into predicate logic, and please don't prove it by making certain number substitution examples!

Problem (Proving theorems!) 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. 3. for any four integers a,b,c,d, two of them are odd and two of them are even, the integer a+b is odd if and only if the integer c+d is odd