Question

Proof by contradiction. If y is odd, y+2 is also odd

Answer 1

yes

Answer 2

Is this correct proof that if y is odd, y+2 is also odd?...

Answer 3

Let's assume that if y+2 is odd, y is even.

therefore y = 2k

2k + 2 is odd according to the first statement (y+2 is odd)

this simplifies to 2(k+1)

However, this is dividable by 2 and thus can only be even. Proving my assumption wrong and thus proving the statement in the question true,

Answer 4

Woops, don't assume the hypothesis is FALSE.
bad bad bad! :O

Just do a direct proof for this one! :)
Assume y is odd.\[\Large \exists \;k \in Z:\qquad y=2k+1\]

Answer 5

Are you supposed to do this by contradiction?
If so, assume the `conclusion` is false.

Answer 6

Assume y+2 is even.
\[\Large \exists\;k \in Z:\qquad y+2=2k\]

Answer 7

Solve for y and show that a contradiction exists! :D

Answer 8

I first tried to show the conclusion as false, but couldn't do it. Showing the hypothesis as false seemed far easier

Answer 9

You're not allowed to do that though :(

Answer 10

Example Statement:
`If it is human` `then it has two hands`.
If we assume the hypothesis is false,
`assume it is not human`
Then we don't care what the result is, it doesn't relate back to our statement in any way.

You assumed that y was even, and ended up with some result.
But that result is not a contradiction...

You proved that if y is even, then y+2 is even.
That doesn't tell us anything about y odd.