All men are mortal. Example: 1. This is not a terrible argument. This is a logic book. View 1A - Propositional Logic.pdf from CS 2212 at Vanderbilt University. But it doesn’t cover the central metalogical results one normally covers in a mathematical logic course: soundness and completeness in predicate logic, computability, i. Yet, it is possible for someone besides a logic student to read this book. If I(p i) = 0, then p Propositional Logic (zyBooks, Chapter 1.1-1.5) Why Study Logic? Five themes: logic and proofs, discrete structures, combinatorial analysis, induction and recursion, algorithmic thinking, and applications and modeling. View 1A - Propositional Logic.pdf from CS 2212 at Vanderbilt University. ! x��}ے�u�;#��8c6*�Z$E�z �!16g�������Z+��{j��AH The basic connectives are 1 .Negation 2. endobj endobj [ PROPOSITIONAL LOGIC] THE GATEBOOK COMPLETE BOOK FOR GATE preparation 1 www.thegatebook.in Proposition: Proposition is a statement which is either true or false but not both at a time. Truth Values An interpretation I is a function which assigns to any atomic formula p i a truth value I(p i) 2f0;1g: If I(p i) = 1, then p i is called true under the interpretation I. A contradiction is a compound statement that is always false A contingent statement is one that is neither a tautology nor a contradiction For example, the truth table of p v ~p shows it is a tautology. (ᩭ�r���>c�FBC2�;Bv��β�� In more recent times, this algebra, like many algebras, has proved useful as a design tool. Truth Values An interpretation I is a function which assigns to any atomic formula p i a truth value I(p i) 2f0;1g: If I(p i) = 1, then p i is called true under the interpretation I. “Logic” is “the study of the principles of reasoning, especially of the structure of propositions as distinguished �!�a*|ܰo�v�%�Z�5D5���^O���#Q�X����Y�@ȸ ȡ`�~��b�����ێ���xġ�#nF�bl6�lW�8. For example, Chapter 13 shows how propositional logic can be used in computer circuit design. Two parts: ! 3 0 obj A��v�v��Ϊ~�����^���}�����_�z}���/�^ܽ��������?^߾�������v����ݳ���v?����i_R����G΅}��T�ew0�c$��*�d@ڇL` 1 0 obj If I(p i) = 0, then p i is called false under the interpretation I. If your roommate picked up the book and thumbed through it, they would not immediately become a logic student. <>>> <>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> •Recall that people in CS propositional logic, such as: ! note formulas of propositional logic. 3+3=6 3. note formulas of propositional logic. This is a logic book. <> Propositional logic is the simplest logic illustrates basic ideas usingpropositions P 1, Snow is whyte P 2, oTday it is raining P 3, This automated reasoning course is boring P i is an atom or atomic formula Each P i can be either true or false but never both The values true or false assigned to each proposition is called truth value of the proposition. So this book does contain some metalogic (e.g., soundness and completeness proofs in propositional logic and propositional modal logic). SEEM 5750 7 Propositional logic A tautology is a compound statement that is always true. CS 2212 Discrete Structures 1A. while p ^ ~p is a contradiction If a conditional is also a tautology, then it is called an implication Some trees have needles. stream Predicate logic can express these statements and make inferences on them. This is not a terrible argument. 1. Connective: It is used to connect one or more propositions. 2 0 obj You are reading this book. Most people who read this book are logic students. Logic in Computer Science 4. Conjunction 3. X > 3. ! 0.3. ! Logic in Computer Science 4. PREFACE ii Gödel’s incompleteness theorems, and so on. CS 2212 Discrete Structures 1A. Disjunction … <> Most people who read this book are logic students. Statements in Predicate Logic P(x,y) ! :_: You are a logic student. If your roommate picked up the book and thumbed through it, they would not immediately become a logic student. 4 0 obj endobj ! •Recall that people in CS Yet, it is possible for someone besides a logic student to read this book.