CPSC 121 Lecture Notes - Lecture 28: Modus Tollens
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Cpsc 121 lecture #28 more on proof techniques. Topics included: more direct proof practices, big o proofs, indirect proofs, proof by contrapositive, proof by contradiction. If statements are contrapositive of each other, the statements are logically equivalent. If they are logically equivalent, then proving the first statement also proves the second statement. Example from belleville, lecture 28 proof techniques , slide 39: consider the two statements: If the square of an positive integer is even, then its square is even. If the square of a positive integer is odd, then its square is odd: these are logically equivalent because they are contrapositive of each other. The remainder of the proof is a direct proof: watch out: doing a proof while assuming false premises implies false conclusions doesn"t prove anything. So not every student got an above average grade on mt1: patrice"s tips for contradiction success, stumble along until something works.
