Question

Explain contradiction assumptions

Answer 1

The method of proof by contradiction is to assume that a statement is not true and then to show that that assumption leads to a contradiction. In the case of trying to prove P ⇒ Q {\displaystyle P\Rightarrow Q} , this is equivalent to assuming that P ∧ ¬ Q {\displaystyle P\land \lnot Q} That is, to assume that P {\displaystyle P} is true and Q {\displaystyle Q} is false. This is known by its latin reductio ad absurdum (reduction to absurdity), since it ends with a statement that cannot be true.

Answer 2

The contradiction means that it is impossible for both to be true and it is known that the Pythagorean theorem holds. It follows from there that the assumption a + b ≤ c must be false and hence a + b > c, proving the claim.

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