PPT-Section 2.2 Statements, Connectives, and Quantifiers

Objectives Identify English sentences that are statements Express statements using symbols Form the negation of a statement Express negations using symbols Translate a negation represented by symbols into English. brPage 1br Some useful connectives For adding information and also as well as moreover too furthermore For sequencing ideas or events firstly secondly thirdly finally eventually then next meanwh Nested Quantifiers. Needed to express statements with multiple variables . Example 1. : “. x+y. = . y+x. for all real numbers” . . xy. (. x+y. = . y+x. ) . where the domains of . x. and . Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . Connectives are words that connect phrases together to make longer (more interesting!) sentences. Can you think of any?. who. because. however. therefore. although. nevertheless. meanwhile. finally. even though. Chapter 2. Predicates and quantifiers. Can be used to express the meaning of a. . wide range of statements. Allow us to reason and explore relationship between objects. 2. Predicates. statements involving variables, . Definitions. Connectives. Vocabulary. Text discussion. Definitions. Virtual goods. Social network. Sustainable product. A brick and mortar company. Virtual goods. Virtual goods are items that exist and can be bought solely online. (Axel, Jonas, Gustaf, Andreas). Can you write a paragraph which includes some or all of these connectives?. Click here to start. Cause and Effect. Contrasting. Qualifying. Sequencing. Comparing. Illustrating. Teacher’s instructions. STATEMENT: A declarative sentence that is either TRUE or FALSE (but not both at once).. MATH 110 Sec 3-1 Lecture on Statements and Connectives . Examples . of . statements. I ate spinach for lunch today.. Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . Logic and Proof. Fall 2014. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . P(4) . information/report . texts . Layout . Uses headings and sub-headings to categorise information.. Includes tables, illustrations and diagrams to engage the reader.. Uses different font sizes and styles.. Satisfiability. Modulo Theories . Frontiers . of . Computational Reasoning . 2009 . –. MSR Cambridge. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. leads to a processing delay at the connective region itself compared to the underspecified connective suoyi and a facilitation at the subject region Both the epistemic and attitudinal types of stance Adapted from Patrick J. Hurley, . A Concise Introduction to Logic. (Belmont: Thomson Wadsworth, 2008).. Predicate Logic. Before I go on to explain quantifiers, first let me address different ways of symbolizing statements. Previously, we used one letter to symbolize one statement. But there is another way to symbolize certain kinds of statements that are relevant to quantifiers. We can also symbolize statements by symbolizing the predicate and subject separately. .