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. They are used to link one sentence to another or to extend a sentence Task One Some of the connectives above are simp le words others are compound words Words made up of more than one word Put the words in the box into two categories Simple Words Co I am superman.. . MATH 110 Sec 3-1: Statements and Connectives Practice Exercises . I. s this a statement?. I am superman.. Hold this for me.. . MATH 110 Sec 3-1: Statements and Connectives Practice Exercises . Reference. :. Humphrey, S., Love, K., & . Droga. , L. (2011). . Working Grammar: An introduction for secondary English teachers. . Victoria: Pearson.. Lexical cohesion - definitions . Lexical. : (adjective) = the words of a language. Propositional Logic Not Enough. Given the statements: . “All men are mortal.”. “Socrates is a man.”. It follows that “Socrates is mortal.”. This can’t be represented in propositional logic. . Computability and Logic. Boolean Connectives. Truth-Functional Connectives and Boolean Connectives. Connectives are usually called . truth-functional . connectives:. This is because the . truth. . value. The Logic of Quantified Statements. Section 2.3. Multiple Quantifiers . Multiple Quantifiers. A statement may contain multiple quantifiers, ∀,∃ or ∃, ∀.. When multiple quantifiers are encountered treat them as they come, “in order”. 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.. Dr. . Yasir Ali. Predicates. Quantifiers. . Universal Quantifiers . Existential Quantifiers. Negation of Quantifiers. Universal Conditional Statement. Negation of Universal Conditional. Multiple Quantifiers. Satisfiability. Modulo Theories . Frontiers . of . Computational Reasoning . 2009 . –. MSR Cambridge. Leonardo de Moura. Microsoft Research. Symbolic Reasoning. Quantifiers in . Satisfiability. Computability and Logic. Boolean Connectives. Truth-Functional Connectives and Boolean Connectives. Connectives are usually called . truth-functional . connectives:. This is because the . truth. . value. Section 1.4. Section Summary. Predicates . Variables. Quantifiers. Universal Quantifier. Existential Quantifier. Negating Quantifiers. De Morgan’s Laws for Quantifiers. Translating English to Logic. (First order Logic). Find the proposition whose Truth Table column is give.. Another form. Some slides have been taken from the sites. http://cse.unl.edu/~choueiry/S13-235/. and . http://. www.whitman.edu. Exercise 4. Exercise . Translate . these statements into English, where C(x) is “. x. . is a comedian” and F(x) is “x is funny” and the domain . consists . of all people. . . a)∀. x(C(x)→F(x)) . 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. .