Proof by contradiction Study guides, Revision notes & Summaries

What is the notation for subset? ⊆ A collection of objects is known as a set What is the notation for integers? ℤ What is the notation for element? ∈ What is the notation for set-roster? { } Write the set-builder notation for, "Numbers whose square roots are an integer" { x | √x ∈ ℤ} Write the set-builder notation for "the set of all x's, such that x is greater than 0" { x | x > 0} T/F: Order matters in ordered pairs? T...

WGU C959 - Discrete Math Questions and Answers Rated A+ What is the notation for subset? ⊆ A collection of objects is known as a set What is the notation for integers? ℤ What is the notation for element? ∈ What is the notation for set-roster? { } Write the set-builder notation for, "Numbers whose square roots are an integer" { x | √x ∈ ℤ} Write the set-builder notation for "the set of all x's, such that x is greater than 0" { x | x > 0} T/F: Order matters in ordered pairs?...

October/November 2020 PLS 1501 Introduction to Western Philosophy 100 Marks Duration: 24 Hours This paper consists of 2 pages including this cover page. Instructions: Your exam consists of 3 QUESTIONS. SECTION A which consists of ONE QUESTION is COMPULSORY and counts 50 marks You can choose to answer ANY TWO of the FOUR QUESTIONS under SECTION B All 3 answers must be submitted as part of A SINGLE word file/ text DOCUMENT. Please remember to download the plagiarism declara...

IBDP Mathematics: Analysis and Approaches, Higher Level Paper 3 Practice Questions Daniel Hwang Suggestions and corrections are welcome. Updated March 18, 2021 Question number  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2 5 2 6 Maximum mark  3 1 3 1 2 7 24 31 2 3 2 9 31 2 7 26 2 3 31 29 2 8 23 2 5 30 2 4 23 32 2 4 2 3 29 23 2 7 3 2 Number & algebra Sequences & series x x x x x x x Exponents & logs x x x x x x x ...

Form When an argument has been translated from English using symbols Invalid Describes an argument when the conclusion is false in a situation with all the hypotheses are are true Valid Describes an argument when the conclusion is true whenever the hypotheses are all true Conclusion The final proposition Hypothesis Each of the propositions within an argument Argument Sequence of propositions Two Player Game In reasoning whether a quantified statem...

WGU C959 unit 1 latest 2023 already passed p∧q conjunction "and" T/T=T T/F=F F/T=F F/F=F p∨q disjunction/inclusive or "or" T/T=T T/F=T F/T=T F/F=F p⊕q exclusive or "or" T/T=F T/F=T F/T=T F/F=F ¬p negation "not" ¬T = F ¬F = T p→q conditional operation "if p then q" T/T=T T/F=F F/T=T (p=F, q=T regardless of truth value) F/F=T converse of p→q q→p contrapositive of p→q ¬q→¬p inverse of p→q ¬p→¬q p↔q biconditional operation "if and only if" T/T=...

Praxis 5039 Questions and Answers Already Passed Paradox a contradiction or dilemma Myth A traditional story about gods, ancestors, or heroes, told to explain the natural world or the customs and beliefs of a society. Oxymoron A figure of speech that combines opposite or contradictory terms in a brief phrase. Essay A piece of prose writing, usually short, that deals with a subject in a limited way and expresses a particular point of view. Malapropism the unintentional misuse...

Exclusive or. ⊕ One or the other, but not both. We can go to the park or the movies. inclusive or is a: disjunction Order of operations in absence of parentheses. 1. ¬ (not) 2. ∧ (and) 3. ∨ (or) the rule is that negation is applied first, then conjunction, then disjunction: truth table with three variables see pic 2^3 rows proposition p → q Ex: If it is raining today, the game will be cancelled. Converse: q → p If the game is cancelled...

Proof by Exhaustion Prove the statement by checking each element individually. Unlike proof by cases, exhaustive proof looks at every case in a way that is not general. Proof by Counterexample Used to disprove a universal statement. For example, to disprove the statement, "All prime numbers are odd" find one example where this statement is false—the number 2—which is both even and prime. Direct Proof In the direct proof, we assume the hypothesis p is true and we try to pro...

Paradox - a contradiction or dilemma Myth - A traditional story about gods, ancestors, or heroes, told to explain the natural world or the customs and beliefs of a society. Oxymoron - A figure of speech that combines opposite or contradictory terms in a brief phrase. Essay - A piece of prose writing, usually short, that deals with a subject in a limited way and expresses a particular point of view. Malapropism - the unintentional misuse of a word by confusion with one that sounds sim...