Logics Logics Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Contents Propositional Logic Logical Equivalences Exercise 1 1 Chapter 1 Logics Discrete Structures for Computing on August 25, 2017 H[.]
Logics Chapter Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Logics Discrete Structures for Computing on August 25, 2017 Contents Propositional Logic Logical Equivalences Exercise Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Faculty of Computer Science and Engineering University of Technology - VNUHCM htnguyen@hcmut.edu.vn 1.1 Logics Contents Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Propositional Logic Contents Propositional Logic Logical Equivalences Logical Equivalences Exercise Exercise 1.2 Logics Course outcomes Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Course learning outcomes L.O.1 Understanding of logic and discrete structures L.O.1.1 – Describe definition of propositional and predicate logic L.O.1.2 – Define basic discrete structures: set, mapping, graphs L.O.2 Represent and model practical problems with discrete structures L.O.2.1 – Logically describe some problems arising in Computing L.O.2.2 – Use proving methods: direct, contrapositive, induction L.O.2.3 – Explain problem modeling using discrete structures Contents L.O.3 Understanding of basic probability and random variables L.O.3.1 – Define basic probability theory L.O.3.2 – Explain discrete random variables L.O.4 Compute quantities of discrete structures and probabilities L.O.4.1 – Operate (compute/ optimize) on discrete structures L.O.4.2 – Compute probabilities of various events, conditional ones, Bayes theorem Propositional Logic Logical Equivalences Exercise 1.3 Logics Logic Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Definition (Averroes) The tool for distinguishing between the true and the false Contents Propositional Logic Definition (Penguin Encyclopedia) The formal systematic study of the principles of valid inference and correct reasoning Logical Equivalences Exercise Definition (Discrete Mathematics - Rosen) Rules of logic are used to distinguish between valid and invalid mathematical arguments 1.4 Logics Applications in Computer Science Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung • Design of computer circuits Contents • Construction of computer programs • Verification of the correctness of programs • Constructing proofs automatically Propositional Logic Logical Equivalences Exercise • Artificial intelligence • Many more 1.5 Logics Propositional Logic Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Definition A proposition is a declarative sentence that is either true or false, but not both Contents Propositional Logic Examples Logical Equivalences Exercise • Hanoi is the capital of Viet Nam • New York City is the capital of USA • 1+1=2 • 2+2=3 1.6 Logics Examples Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Examples (Which of these are propositions?) • How easy is logic! Contents • Read this carefully • H1 building is in Ho Chi Minh City • 4>2 Propositional Logic Logical Equivalences Exercise • 2n ≥ 100 • The sun circles the earth • Today is Thursday • Proposition only when the time is specified 1.7 Logics Notations Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Contents • Propositions are denoted by p, q, • The truth value (”chân trị”) is true (T) or false (F) Propositional Logic Logical Equivalences Exercise 1.8 Logics Operators Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Negation - ”Phủ định”: ¬p Contents Propositional Logic Bảng: Truth Table for Negation Logical Equivalences Exercise p ¬p T F F T 1.9 Logics Operators Huynh Tuong Nguyen, Nguyen An Khuong, Vo Thanh Hung Conjunction - ”Hội”: p ∧ q “p and q” Disjunction - ”Tuyển”: p ∨ q “p or q” Contents p q p∧q p q p∨q T T F F T F T F T F F F T T F F T F T F T T T F I’m teaching DM1 and it is raining today Propositional Logic Logical Equivalences Exercise We need students who have experience in Java or C++ Tomorrow, I will eat Pho or Bun bo 1.10