INTRODUCTION TO MATHEMATICAL LOGIC AND DIFFERENT UNDERSTANDINGS, Schemes and Mind Maps of Mathematical logic

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Foundations of Mathematical Logic Module 1. Prop itional Logic [i Module 1 Propositional Logic Introduction Welcome to Module 1. This module covers topics found in the area of logic that deals with propositions, called propositional logic or propositional calculus. The discussions will start with an introduction of the basic building blocks of logic, called propositions. This will be followed by discussions on the different methods in constructing compound propositions using one or more logical operators, such as negation, conjunction, disjunction, implication and bi-implication, and discussions on the different rules in determining truth values of compound propositions. Procedures in constructing truth tables will be illustrated, and new terminologies such as tautology, contradiction, contingency, and logical equivalence will be defined. Lastly, the use of two-column proofs will be introduced to prove logical equivalences. This module contains four lessons, entitled: Proposition; Logical Operators and Compound Propositions; Tautology, Contradiction and Contingency; and Logical Equivalences. Each lesson is composed of different sections, which serve specific roles. Concepts are formally defined in Definition sections, and these are followed by discussion sections and Example sections, wherein concepts are discussed and illustrated in detail. Each lesson ends with formative assessment questions found in the Try this! sections. Suggested answers for the formative assessments are found in the Check your work! section which is located in the last pages of this module. Lastly, Wrap it up! section is given after the discussions of the last lesson for you to summarize the main points discussed in this module. Objectives This module aims to help you accurately do each of the following: Identify a proposition and determine its truth value; Construct a compound proposition; Determine the truth value of a compound proposition; Identify tautologies, contradictions and contingencies using truth tables; Prove a logical equivalence using truth table; and Prove a logical equivalence using two-column proof. ay aye LOGIC AND SET THEORY CYRENE A. CASPE / LEYTE NORMAL UNIVERSITY