Suppose you are giving a direct proof of the statement \"For all integers n, if

Question

Suppose you are giving a direct proof of the statement "For all integers n, if n is odd, then n3 + 6 is odd." Which
one of the following is a correct way to begin the proof?

Assume that n is an even integer and, hence,
that there is an integer k such that n = 2k.

Assume that n is an odd integer and, hence,
that there is an integer k such that n = 2k + 1.

Assume that n is an integer such that n3 + 6 is even and, hence,
that there is an integer k such that n3 + 6 = 2k.

Assume that n is an integer such that n3 + 6 is odd and, hence,
that there is an integer k such that n3 + 6 = 2k + 1.

Explanation / Answer

Since it is case of of direct proof we need to first assume our hypthesis and then proof the result.

Option 4 is correct in this case.

Assume that n is an integer such that n3 + 6 is odd and, hence,
that there is an integer k such that n3 + 6 = 2k + 1.

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