Consider the statement:
"For any integers x and y, if xy+x is odd, then x is odd."
The following is a "proof":
Proof:
Let x and y be integers.
If x is odd, then there is an integer p such that x=2p+1.
Then xy+x = (2p+1)y+(2p+1) = 2(py+p) + y+1 .
But if y is odd, then 2(py+p)+y+1 is even.
Thus the statement is false.
Which of the following is true?

Question

Consider the statement:

"For any integers x and y, if xy+x is odd, then x is odd."

The following is a "proof":

Proof:

Which of the following is true?

Accepted Answer

The proof is incorrect. It shows that the converse is false.

Accepted Answer

The proof is incorrect. There is an error on line 2: it assumes what we are trying to prove.

Answer

The proof is incorrect. There is an algebraic error on line 3.

Answer

The proof is correct. The statement is false.

Answer

The proof is correct. It is a proof by contrapositive.

Answer

The proof is correct. It is a proof by contradiction.

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