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Lecture Discrete mathematics and its applications - Lecture 2

In this lesson, you will leam about specific steps you can take to secure your computer system and your data from a variety of threats. You might be surprised to learn that computer security is not primarily a technical issue, and is not necessarily expensive. For the most part, keeping your system and data secure is a matter of common sense. | The Foundations: Logic and Proofs Chapter 1, Part I: Propositional Logic With Question/Answer Animations Copyright © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter Summary Propositional Logic The Language of Propositions Applications Logical Equivalences Predicate Logic The Language of Quantifiers Logical Equivalences Nested Quantifiers Proofs Rules of Inference Proof Methods Proof Strategy Propositional Logic Summary The Language of Propositions Connectives Truth Values Truth Tables Applications Translating English Sentences System Specifications Logic Puzzles Logic Circuits Logical Equivalences Important Equivalences Showing Equivalence Satisfiability Propositional Logic Section 1.1 Section Summary Propositions Connectives Negation Conjunction Disjunction Implication; contrapositive, inverse, converse Biconditional Truth Tables Propositions A proposition is a declarative sentence that is either true or false. Examples of propositions: The Moon is made of green cheese. Trenton is the capital of New Jersey. Toronto is the capital of Canada. 1 + 0 = 1 0 + 0 = 2 Examples that are not propositions. Sit down! What time is it? x + 1 = 2 x + y = z Propositional Logic Constructing Propositions Propositional Variables: p, q, r, s, The proposition that is always true is denoted by T and the proposition that is always false is denoted by F. Compound Propositions; constructed from logical connectives and other propositions Negation ¬ Conjunction ∧ Disjunction ∨ Implication → Biconditional ↔ Compound Propositions: Negation The negation of a proposition p is denoted by ¬p and has this truth table: Example: If p denotes “The earth is round.”, then ¬p denotes “It is not the case that the earth is round,” or more simply “The earth is not round.” p ¬p T F F T Conjunction The conjunction of propositions p and q is denoted by p ∧ q and has this truth table: Example: If p denotes “I am . | The Foundations: Logic and Proofs Chapter 1, Part I: Propositional Logic With Question/Answer Animations Copyright © McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter Summary Propositional Logic The Language of Propositions Applications Logical Equivalences Predicate Logic The Language of Quantifiers Logical Equivalences Nested Quantifiers Proofs Rules of Inference Proof Methods Proof Strategy Propositional Logic Summary The Language of Propositions Connectives Truth Values Truth Tables Applications Translating English Sentences System Specifications Logic Puzzles Logic Circuits Logical Equivalences Important Equivalences Showing Equivalence Satisfiability Propositional Logic Section 1.1 Section Summary Propositions Connectives Negation Conjunction Disjunction Implication; contrapositive, inverse, converse Biconditional Truth Tables Propositions A proposition is a declarative sentence that is