Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, Slide Logic The Study of What’s True or False or Somewhere in Between
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, Slide 2 Statements, Connectives, and Quantifiers 3.1 Identify statements in logic Represent statements symbolically using five connectives (continued on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 3.1, Slide 3 Statements, Connectives, and Quantifiers 3.1 Understand the difference between the universal and existential quantifiers Write the negations of quantified statements
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 4 Statements in Logic In symbolic logic, we only care whether statements are true or false – not their content.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 5 Statements in Logic Examples of statements:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 6 Statements in Logic Examples of non-statements:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 7 Statements in Logic Note that (a)-(d) fall into 2 categories: –Simple statements containing a single idea ((a) and (c)). –Compound statements containing several ideas ((b) and (d)).
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 8 Statements in Logic
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 9 Connectives The connectives used in logic generally fall into five categories: –Negation –Conjunction –Disjunction –Conditional –Biconditional
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 10 Connectives (example on next slide)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 11 Connectives Negation Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 12 Connectives Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 13 Connectives
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 14 Connectives Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 15 Connectives Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 16 Connectives Example:
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 17 Connectives
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 18 Quantifiers A quantifier tells us “how many” and fall into two categories. –Universal quantifiers –Existential quantifiers
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 19 Quantifiers
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 20 Quantifiers
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 21 Negating Quantifiers Suppose we want to negate the statement “All professional athletes are wealthy.” (universal) Correct: “Some athletes are not wealthy” or “Not all athletes are wealthy.” (both existential) Incorrect: “All athletes are not wealthy.” (universal)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 22 Negating Quantifiers Negate the statement “Some students will get a scholarship.” (existential) Correct: “No students will get a scholarship.” (universal) Incorrect: “Some students will not get a scholarship.” (existential)
Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 3.1, Slide 23 Negating Quantifiers