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). 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.
Ppt Proofs Powerpoint Presentation Free Download Id 3387509 Proof by cases is used for statements of the form for all , x ∈ d, p (x), where the set d can be broken into smaller sets. for example, a statement might be easier to prove for even numbers and odd numbers separately, rather than more general integers. 🔗. every truth table represents all possible cases of true and false for a logical. Two examples of using the proof by cases method.leave any questions comments below!keep flexin' those brain muscles!facebook: facebook brain. Case 1.2: some pair among those people have met each other. then that pair, together with x, form a club of 3 people. so the theorem holds in this subcase. this implies that the theorem holds in case 1. case 2: suppose that at least 3 people did not meet x. this case also splits into two subcases: case 2.1: every pair among those people met. Figure 22.1 figure for proof about three points lying on a line or a circle. theorem. let x, y and z be points in the plane. then, all lie on. a line or all lie on a circle. tip: “or” statements lend themselves to proof by cases. tip: extreme examples lend themselves to proof by cases. all be on a line.
Discrete Math Methods Of Proof Ppt Video Online Download Case 1.2: some pair among those people have met each other. then that pair, together with x, form a club of 3 people. so the theorem holds in this subcase. this implies that the theorem holds in case 1. case 2: suppose that at least 3 people did not meet x. this case also splits into two subcases: case 2.1: every pair among those people met. Figure 22.1 figure for proof about three points lying on a line or a circle. theorem. let x, y and z be points in the plane. then, all lie on. a line or all lie on a circle. tip: “or” statements lend themselves to proof by cases. tip: extreme examples lend themselves to proof by cases. all be on a line. 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. Steps for proof by cases. mutual exhaustion: show that there is a set of cases that is mutually exhaustive. prove each case: prove that the statement is true in each of the provided cases. example. the statement below will be demonstrated by a proof by cases. for any integer k, the product 3k^2 k is even. mutual exhaustion any integer is.
Ppt Methods Of Proof Powerpoint Presentation Free Download Id 226798 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. Steps for proof by cases. mutual exhaustion: show that there is a set of cases that is mutually exhaustive. prove each case: prove that the statement is true in each of the provided cases. example. the statement below will be demonstrated by a proof by cases. for any integer k, the product 3k^2 k is even. mutual exhaustion any integer is.
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