Channel: Bisqwit

Category: Education

Tags: natural deductionnegationpropositional logicbisqwitexistential quantifieruniversal quantifierconjunctioninversionpearswhite carfor-everyoneimplicationkiwisenginesboolean algebradigital electronicsfallacytutorialmodus ponensfor-allnobodywhite carsequivalencede morgan's lawcar has an enginedisjunctionjoel yliluomathere-existspredicate logiceveryone likes kiwisboolean logiclogic gatesmodus tollensmilo likes pearssomeoneturnstile

Description: In this four-part series we explore propositional logic, Karnaugh maps, implications and fallacies, predicate logic, existential and universal quantifiers and finally natural deduction. Become a member: youtube.com/Bisqwit/join My links: Twitter: twitter.com/RealBisqwit Liberapay: liberapay.com/Bisqwit Patreon: patreon.com/Bisqwit (Other options at bisqwit.iki.fi/donate.html) Twitch: twitch.tv/RealBisqwit Homepage: iki.fi/bisqwit *Summary of the introduction and elimination rules.* Here [M]→N means that by temporarily assuming that M is true you can conclude N. If N is already true, you can just use N directly and ignore M. If you already know M is true (for example it is a premise), you should not mark it temporary. “Is valid” means that you can make that conclusion. “Is true” means that the expression has already been concluded or given as a premise. INTRODUCTION RULES: I Conjunction/AND:  If P and Q, then P∧Q is valid. I Disjunction/OR:  If P, then P∨Q is valid.  If Q, then P∨Q is valid. I Biconditional/equivalence (↔):  If [P]→Q and [Q]→P, then P↔Q is valid. I Implication (→):  If [P]→Q, then P→Q is valid. I Negation (NOT):  If [P]→(Q∧¬Q), then ¬P is valid. I Universal quantifier (∀):  If P is true independent of x, then ∀xP is valid. I Existential quantifier (∃):  If P(y), then ∃xP(x) is valid for some independent variable x. ELIMINATION RULES: E Conjunction (AND):  If P∧Q, then P is valid.  If P∧Q, then Q is valid. E Disjunction (OR):  If P∨Q, and [P]→R and [Q]→R, then R is valid. E Biconditional/equivalence (↔):  If P↔Q, and P is true, then Q is valid.  If P↔Q, and Q is true, then P is valid. E Implication (→):  If P→Q, and P is true, then Q is valid. E Negation (NOT):  If ¬¬P, then P is valid. E Universal quantifier (∀):  If ∀xP(x), then P(y) is valid for some independent variable y. E Existential quantifier (∃):  If ∃xP, and [P]→Q independent of x, then Q is valid. CONTENTS: 0:00 Introduction 1:05 Rules for Conjunction (AND) 1:31 Rules for Disjunction (OR) 1:32 What is the point? Axioms! 3:18 Example 1: Can we swap A and B? 4:50 Example 2: Deconstructing OR 5:38 Rules for Implication (IMP) 6:44 Rules for Equivalence (XNOR) 7:24 Example 3: From equivalence to implication 9:28 Rules for Negation (NOT) 10:49 Temporary Assumptions Workshop 12:06 Example 4: Creating a contradiction 14:12 Rules for Existential Quantifier (∃) 15:00 Rules for Universal Quantifier (∀) 15:28 Bound and Free Variables 17:34 Summary 17:53 Example 5: Is tiger a mammal? 20:03 Conclusion 20:21 Example 6: Every likes kiwis, Milo might like pears 24:38 Example 7: For all, A is true ⇒ For nobody, A is false 31:10 Example 8: White cars and engines 35:53 Example 9: Proving a negative? 38:51 Links