- #1

- 520

- 2

## Main Question or Discussion Point

It can be proved by proof by contradiction. hence it is just a variant of it?

- Thread starter tgt
- Start date

- #1

- 520

- 2

It can be proved by proof by contradiction. hence it is just a variant of it?

- #2

- 283

- 3

- #3

CRGreathouse

Science Advisor

Homework Helper

- 2,820

- 0

Proof by contradiction: Assume p and ¬q; prove ⊥.

Proof by contraposition: Assume ¬q; prove ¬p.

A proof by contraposition can be turned into a proof by contradiction by adding the step "p ∧ ¬p ⇒ ⊥". But proofs by contradiction don't need to prove ¬p as an intermediate step; they can prove contradiction in other ways. So proof by contradiction is stronger.

On the other hand, the more constrained proof by contraposition is considered a constructive technique, while proof by contradiction is always considered nonconstructive. So if you have a choice use contraposition.

- #4

HallsofIvy

Science Advisor

Homework Helper

- 41,793

- 922

However, "proof by contradiction" more general. You start with "if not Q" but only need to arrive at two statements that contradict one another. I have seen proofs in which the two contraditory statements have no apparent connection with the hypothesis, P.

- Replies
- 3

- Views
- 1K

- Last Post

- Replies
- 7

- Views
- 5K

- Replies
- 2

- Views
- 969

- Last Post

- Replies
- 2

- Views
- 3K

- Last Post

- Replies
- 9

- Views
- 929

- Last Post

- Replies
- 3

- Views
- 1K

- Replies
- 7

- Views
- 830