test 1 review

# test 1 review - numbers to sum is 1+ 1, which doesnt equal...

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Click to edit Master subtitle style 4/21/10 Discrete Mathematics Test 1 Review Session

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4/21/10 Direct Proof Proof by Contraposition Proof by Contradiction Exhaustive Proof Existence Proof Uniqueness Proof Proof Techniques
4/21/10 Common Proof Notation

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4/21/10 Easy Proofs
4/21/10 Direct Proof

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4/21/10 Proof by Contraposition
4/21/10 Proof by Contraposition

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4/21/10 Proof by Contradiction The Sock Problem

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4/21/10 Proof by Contradiction The Sock Problem
4/21/10 Look at all possible cases Prove that the theorem holds in each specific case Exhaustive Proof

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4/21/10 Prove that no perfect cube that is less than 1000 is the sum of 2 other perfect cubes Cases: 1, 8, 27, 64, 125, 216, 343, 512, 729 1: Theorem holds because there aren’t 2 perfect cubes less than 1 that could possibly sum to 1 8: Theorem holds because the only option for

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Unformatted text preview: numbers to sum is 1+ 1, which doesnt equal 8 Other options: check all possible Exhaustive Proof 4/21/10 Constructive You only need to show a single example that satisfies the condition given in the theorem Nonconstructive Show that it wouldnt be possible for such an element to not exist Usually leverage proof by contradiction Existence Proofs 4/21/10 Constructive Existence Proof 4/21/10 Nonconstructive Existence Proof 4/21/10 Step 1: prove existence Step 2: prove uniqueness Any element that has the desired property must be the same as the element discovered by the uniqueness proof Uniqueness Proof 4/21/10 Uniqueness Proof 4/21/10 Basics of Sets 4/21/10 Basics of Sets 4/21/10 Set Operations...
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## This note was uploaded on 04/21/2010 for the course MA 2201 taught by Professor Peterchristopher during the Spring '10 term at WPI.

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test 1 review - numbers to sum is 1+ 1, which doesnt equal...

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