Discrete Math 1 8 1 Proof By Cases Youtube 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. Please see the updated video at youtu.be dheujkusnyithe full playlist for discrete math i (rosen, discrete mathematics and its applications, 7e) can.
Discrete Math 1 8 1 Proof By Cases Youtube 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. 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). Proof by cases case 1: a ≥ b ≥ c (a @ b) = a, a @ c = a, b @ c = b hence (a @ b) @ c = a = a @ (b @ c) therefore the equality holds for the first case. a complete proof requires that the equality be shown to hold for all 6 cases. but the proofs of the remaining cases are similar. try them. 4. This is a theorem you can refer to in later work. the proof of this theorem illustrates a technique called "proof by cases". proof. let \(n\) be any integer. \(n 1\) is the next consecutive integer, by the meaning of consecutive. we will consider two cases. case 1: \(n\) is even.
Proof By Cases Explained W 5 Logic Examples Proof by cases case 1: a ≥ b ≥ c (a @ b) = a, a @ c = a, b @ c = b hence (a @ b) @ c = a = a @ (b @ c) therefore the equality holds for the first case. a complete proof requires that the equality be shown to hold for all 6 cases. but the proofs of the remaining cases are similar. try them. 4. This is a theorem you can refer to in later work. the proof of this theorem illustrates a technique called "proof by cases". proof. let \(n\) be any integer. \(n 1\) is the next consecutive integer, by the meaning of consecutive. we will consider two cases. case 1: \(n\) is even. 13.1 steps. the steps in a proof by cases are similar to those in a proof by exhaustion: perform a partition of \(p\) into cases. note that a partition of \(p\) into “cases” is similar to the list of possibilities you create for a proof by exhaustion, except that cases are generally more broad (usually containing multiple elements) than each single possibility in a proof by exhaustion. We do a problem that could be done with cases, but is easier as a direct proof. we also then look at a proof with min and max that requires cases.like and sh.
Discrete Mathematics Proof By Case Youtube 13.1 steps. the steps in a proof by cases are similar to those in a proof by exhaustion: perform a partition of \(p\) into cases. note that a partition of \(p\) into “cases” is similar to the list of possibilities you create for a proof by exhaustion, except that cases are generally more broad (usually containing multiple elements) than each single possibility in a proof by exhaustion. We do a problem that could be done with cases, but is easier as a direct proof. we also then look at a proof with min and max that requires cases.like and sh.
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