Final answer:
To prove the statement by contrapositive, we need to show that if a is not odd or b is not odd, then ab is not odd. Assuming a is even or b is even, we can write them as a = 2k and b = 2m, respectively. Multiplying a and b, we get ab = (2k)(2m) = 4km. Since 4 is even, 4km is also even. Therefore, if a is even or b is even, then ab is even.
Step-by-step explanation:
To prove the statement by contrapositive, we need to show that if a is not odd or b is not odd, then ab is not odd.
Assume that a is even or b is even. If a is even, it can be written as a = 2k, where k is an integer. Similarly, if b is even, it can be written as b = 2m. Multiplying a and b, we get ab = (2k)(2m) = 4km. Since 4 is even, 4km is also even. Therefore, if a is even or b is even, then ab is even. By contrapositive, if ab is odd, then a is odd and b is odd.