Use the definitions in Exercise (9) to help write a proof for each of the fol- lowing statements: * (a) If a and b are both type 1 integers, then a + b is a type 2 integer. (b) If a and b are both type 2 integers, then a + b is a type 1 integer. (c) If a is a type 1 integer and b is a type 2 integer, then a - b is a type 2 integer. (d) If a and b are both type 2 integers, then a - b is type 1 integer. An integer a is said to be a type 0 integer if there exists an integer n such that a = 3n. An integer a is said to be a type 1 integer if there exists an integer n such that a = 3n + 1. An integer a is said to be a type 2 integer if there exists an integer m such that a = 3m +2. a 3D