Proofs

Question 1

Proofs that assume a statement to be true.

Answer 1

Direct Proofs

Question 2

Proofs by contradiction. Proofs that assume a statement to be false. The purpose of such a proof is to show that a hypothesis is false, given the negation of the conclusion, indicating that the conclusion must be true.

Answer 2

Indirect Proofs

Question 3

A proof written in the form ⌐Q → ⌐P. It seeks to show that the negation of Q will yield the negation of P.

Answer 3

Proof by Contraposition

Question 4

A proof written in the form, P ∧ ⌐Q. It seeks to show the negation of Q will result in a false hypothesis, indicating that the conclusion of the statement, as written, must be true. In other words P → Q is true.

Answer 4

Proof by Contradiction