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Mathematical Reasoning
Brock University
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Basil Nanayakkara

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MATH 1P66 Lecture 1: Propositional Logic

MATH 1P66 Lecture Notes - Lecture 1: Logic Gate, Truth Table, Or Gate

A proposition is declarative sentence that is either true or false, but not both. Winnipeg is the capital of canada (false: everest is the tallest moun

MATH 1P66 Lecture Notes - Lecture 1: Propositional Variable, The Foundations, Truth Table

Mid term test (sat oct 20 1:00-3:00pm) 40% Definition: a proposition is a declarative sentence that is either true or false, but not both. 1- winnipeg

MATH 1P66 Lecture Notes - Lecture 2: Idempotence

This makes making truth tables for more complicated compound propositions cumbersome, so propositional equivalences, equivalent propositions that can r

MATH 1P66 Lecture 2: Math Lecture #2

P q if p, then q q, unless not p. A biconditional denoted by p q is the statement. If p and only if q p iff q p implies q, and conversely p is necessa

MATH 1P66 Lecture 2: Propositional Logic 2

MATH 1P66 Lecture 3: Propositional Equivalencies

MATH 1P66 Lecture 3: Math Lecture #3

Definition- a compound proposition that is always true, regardless of the truth values of the propositional variables appearing in it, is called a taut

MATH 1P66 Lecture Notes - Lecture 4: Existential Quantification, Propositional Function, First-Order Logic

Predicates are propositions functions that are rather similar to algebraic functions. The predicate part of the propositional function refers to a prop

MATH 1P66 Lecture Notes - Lecture 4: Universal Quantification, Existential Quantification, Propositional Function

#16 b) prove t or f (p q) ^ (q r) (p r) remember: p q = q v p. = rv p v [(qv p)^(rv q)] remember: (p^q) = p v q. = rv p v (qv p) ^ (rv q) disjunctions

MATH 1P66 Lecture 4: Intro to Predicates and Quantifiers

MATH 1P66 Lecture 5: Math Lecture #5

Negation: xp(x) (cid:3247)there is a flower that is not red(cid:3248) Xp(x) = x p(x: n(x): x has visited north dakota domain={students at brock u, xn(x

MATH 1P66 Lecture Notes - Lecture 6: Counterexample

Xp(x) = x p(x) demorgan"s law for quantifiers: domain = r, x(-2<x<3) = x[(x(cid:3639)-2)v(x(cid:3640)3): domain = z find counter example where possible

MATH 1P66 Lecture 6: Predicates and Quantifiers and NESTED QUANTIFIERS

MATH 1P66 Lecture Notes - Lecture 6: Propositional Function

Nested quantifiers are when we have one (or more) quantifier(s) in the scope of another quantifier. The order of universal or existential quantifiers i

MATH 1P66 Lecture 7: Math Lecture #7 Week 4

Write using predicates and quantifiers as well as other logical equations: he sum of two negative integers is negative. Domain = z set of all integers.

MATH 1P66 Lecture 7: NESTED QUANTIFIERS - Continued

MATH 1P66 Lecture 8: INTRODUCTION TO PROOFS

MATH 1P66 Lecture Notes - Lecture 8: Contraposition

Instead of proving p q, we prove the contrapositive q p. (x(cid:3640)1)^ (y(cid:3640)1) x+y<2 (x<1)^(y<1) x+y<2 x<1 y<1 x+y<2. Add

MATH 1P66 Lecture 9: Direct Proofs and Contradiction

MATH 1P66 Lecture Notes - Lecture 9: Year 2000 Problem

A proof is a valid argument that establishes the truth of a mathematical statement. Start with the hypothesis p and use the definitions, axioms and pre

MATH 1P66 Lecture 12: Proof Methods and Strategy

MATH 1P66 Lecture 13: Proof Methods and Strategy

MATH 1P66 Lecture 14: Sets Of Functions

MATH 1P66 Lecture 15: SETS PART 2

MATH 1P66 Lecture 16: Sets Part 3 (Laws and Venn Diagrams)

MATH 1P66 Lecture 17: Generalized Unions & Intersections

MATH 1P66 Lecture 18: Sets: Functions

MATH 1P66 Lecture 19: Function Part 2

MATH 1P66 Lecture 20: Mathematical Induction

MATH 1P66 Lecture 21: Mathematical Induction Part 2

MATH 1P66 Lecture 22: Mathematical Induction and Divisibility

MATH 1P66 Lecture 23: Divisibility Problems

MATH 1P66 Lecture 24: Strong Induction

MATH 1P66 Lecture 25: Boolean Arithmetic