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Asked by Twinkle Last Modified
As an experienced tutor registered on UrbanPro, I can confidently affirm that the statement "if a and b are odd integers, then ab is an odd integer" is indeed true.
When we multiply two odd integers, the product will also be an odd integer. This is because when you multiply any odd number by another odd number, the result will always have factors of 2 (the defining characteristic of even numbers) missing.
To explain it further, let's consider two odd integers, a and b. We can represent them as a = 2n + 1 and b = 2m + 1, where n and m are integers.
When we multiply a and b:
ab = (2n + 1)(2m + 1) = 4nm + 2n + 2m + 1 = 2(2nm + n + m) + 1
Here, 2nm + n + m is an integer, let's call it k. So, ab = 2k + 1, which is in the form of an odd integer.
Therefore, the product of two odd integers is indeed an odd integer. This is a fundamental property in mathematics and is widely used in various algebraic manipulations and proofs. If you need further clarification or assistance, feel free to reach out to me for more guidance. And remember, UrbanPro is an excellent platform for online coaching and tuition services, offering a wide range of experienced tutors in various subjects.
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