Proof By Cases Explained W 5 Logic Examples Introduction to video: proof by cases. 00:00:57 overview of proof by exhaustion with example #1. exclusive content for members only. 00:14:41 prove if an integer is not divisible by 3 (example #2) 00:22:28 verify the triangle inequality theorem (example #4) 00:26:44 the sum of two integers is even if and only if same parity (example #5). Published dec 19, 2023. contribute to docs. proof by cases is a technique used in mathematical proofs to demonstrate a statement by showing that it is true in each of a set of cases. these cases must be mutually exhaustive, meaning that they cover all possibilities, so that at least one of them must be true. by showing that the statement holds.
Proof By Cases Discrete Math Examples Payment Proof 2020 Exploring a method of proof by exhaustion known as proof by cases.video chapters:introduction 0:00what is a proof by cases? 0:10proof by cases example 1 2:27. This proof is an example of a proof by contradiction, one of the standard styles of mathematical proof. first and foremost, the proof is an argument. it contains sequence of statements, the last being the conclusion which follows from the previous statements. the argument is valid so the conclusion must be true if the premises are true. We look at direct proofs, proof by cases, proof by contraposition, proof by contradiction, and mathematical induction, all within 22 minutes. this video incl. Here are some examples of how you might split up a proof into cases (step 1), depending on what type of number the conjecture concerns: family. possible cases. a ∈ za ∈z. case 1: aa is even. case 2: aa is odd. case 1: a = 3ka = 3k. case 2: a = 3k 1a = 3k 1. case 3: a = 3k 2a = 3k 2.
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