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.

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

answer: what are the answer choices?

step-by-step explanation: