Use a direct proof to show that the product of two odd integers is odd.

Step-by-step explanation:

A direct proof is a method that takes an statement p, which we assume to be true, and use it to show directly that another statement q is true. So this method has the following steps:

Fact that we need to use:

Every odd integer can be written in the form 2m + 1 for some unique other integer m

Let p be the statement a and b be odd integers and q be the statement that the product of a and b is odd.

Proposition if a and b are odd, then the product of a and b is odd

Proof: Assume that a and b are odd integers, the by definition a = 2m + 1 and b = 2n + 1 for some integers m and n. we will now use this to show that the product of a and b is odd.

Hence we have shown that the product of a and b is odd since 2k + 1 is and odd integer. Therefore we have shown that p ⇒ q and so we have completed our proof.

Step-by-step explanation:

The proof by the direct method that the product of two odd numbers is odd integer number, is the following:

Let and be two odd integers, then and , for some integers a and b.

where , which guarantees that is an integer number. In this way, is an odd integer.

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step-by-step explanation:

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step-by-step explanation:

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