Question

If we wanted to prove the following statement using proof by contradiction, what assumption would we start our proof with?

Statement: When $x$ and $y$ are odd integers, there does not exist an odd integer $z$ such that $x+y=z$.

• A. When $x$ and $y$ are odd integers, there does exist an even integer $z$ such that $x+y=z.$
• B. When $x$ and $y$ are odd integers, there does not exist an odd integer $z$ such that $x+y=z$.
• C. When $x$ and $y$ are odd integers, there does exist an odd integer $z$ such that $x+y=z$.
• D. When $x$ and $y$ are odd integers, there does not exist an even integer $z$ such that $x+y=z$.

Answer 1

Answer: (C)

When $x$ and $y$ are odd integers, there does exist an odd integer $z$ such that $x+y=z$.

when we prove by contradiction we need to assume the negation of the initial given statement , on negating the given statement we get When xx and yy are odd integers, there does exist an odd integer zz such that x+y=zx+y=z.which is the answer.

$C$