Prove the following theorems with the method of direct proof. 1. If a and b are both odd numbers, then a - b is an odd number. 2. If a is an even number, then a3 is an even number. 3. If a is an odd number, then a3 is an odd number. Dene the set of rational numbers as follows: m Q={;lm,nEZandn=#0} 4. If a is a rational number and b is a rational number, then a + b is also a rational number. 5. If a and b are both rational numbers such that a at 0 and b at D, then% is also a rational number. 6. If given a sequence of ve consecutive integers (e. g. l,2,3,4,5), then the sum of these integers is always divisible by 5. That is, the result is a multiple of 5