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). When using cases in a proof, the main rule is that the cases must be chosen so that they exhaust all possibilities for an object x in the hypothesis of the original proposition. following are some common uses of cases in proofs. when the hypothesis is, " n is an integer." case 1: n is an even integer. case 2: n is an odd integer.
Ppt Methods Of Proof Powerpoint Presentation Free Download Id 226798 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. 1.7 proof by cases. breaking a complicated proof into cases and proving each case separately is a com mon, useful proof strategy. here’s an amusing example. let’s agree that given any two people, either they have met or not. if every pair of people in a group has met, we’ll call the group a club. if every pair of people in. 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. 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.
Proof By Cases Explained W 5 Logic Examples 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. 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. 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. Explanation. proof by cases can be expressed in natural language as follows: we are given that either ϕ ϕ is true, or ψ ψ is true, or both. suppose we make the assumption that ϕ ϕ is true, and from that deduce that χ χ has to be true. then suppose we make the assumption that ψ ψ is true, and from that deduce that χ χ has to be true.
Proof By Cases 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. Explanation. proof by cases can be expressed in natural language as follows: we are given that either ϕ ϕ is true, or ψ ψ is true, or both. suppose we make the assumption that ϕ ϕ is true, and from that deduce that χ χ has to be true. then suppose we make the assumption that ψ ψ is true, and from that deduce that χ χ has to be true.
Proof By Cases Explained W 5 Logic Examples
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