Question

Which term best describes a proof in which you assume the opposite of what you want to prove?

Answer 1

A proof where you assume the opposite of what you want to prove is usually known as a CONTRADICTORY proof. I hope this answer helps you, and if it does feel free to give me a rate and a thanks :)

Answer 2

Contradictory Statement

Explanation:

In contradictory statement , we basically describes a proof by assuming opposite of what we want to prove .

For example :

Prove that
`√(2)` is irrational .

Solution :

We will prove this by contradiction .

Let if possible
`√(2)` is rational .

`√(2)=(p)/(q)` where p and q are integers and coprime such that
`q\\eq 0`

On squaring both sides , we get

`2q^2=p^2\\\Rightarrow 2|p^2\\\Rightarrow 2|p`

we get ,

p=2r

On squaring both sides, we get

`p^2=4r^2\\\Rightarrow 2q^2=4r^2\\\Rightarrow q^2=2r^2\\\Rightarrow 2|q^2\\\Rightarrow 2|q`

So, 2 divides p and q which is a contradiction to the fact that p and are coprime .

Therefore,
`√(2)` is irrational .