You want to negate the statement "xy and x+y are even". If this statement is not true, it means that either xy is not even or x+y is not even, or both. And "not even" is the same as "odd". So indeed "If x or y is odd then xy or x+y is odd" is correct.bonfire09 said:Homework Statement
The original statement is Prove that if xy and x+y are even then both x and y are even.
The Attempt at a Solution
I think it goes like "If x or y is odd then xy and x+y are odd"? I'm not too sure though because the first "and" in the hypothesis is confusing. I'm not sure if its supposed to go like"If x or y is odd then xy or x+y is odd?
To whom are you responding?bonfire09 said:I would think the sentence would have to be " If x is odd or y is odd then xy is odd or x+y is odd." I think you have it flipped around.
A contrapositive statement is a logical statement that is formed by switching the hypothesis and conclusion of a conditional statement and negating both.
To write a contrapositive statement, first identify the given conditional statement. Then, switch the hypothesis and conclusion of the statement and add the word "not" in front of both parts.
The purpose of finding the contrapositive of a statement is to prove the original statement is logically equivalent to its contrapositive. This can help in simplifying complex statements and making logical arguments.
Yes, a statement and its contrapositive can both be true. This is because they are logically equivalent and have the same truth value. If the original statement is true, the contrapositive will also be true.
The contrapositive of a statement can be used in mathematical proofs to show that a statement is true by proving its contrapositive is true. This is often used in proofs by contradiction, where the negation of a statement is assumed to be true and a contradiction is found, proving the original statement to be true.