Review 7

Review 7 Gongjun Yan

Homework • Homework: uniqueness quantifier • ! P(x) = “there exists a unique x such that P(x) is true” • P59 10.h • x !y f(x,y) • Page 37 • P59 12.L • x y (x!=y^ c(x,y) ^c(y,x)) • P49 46 • P73 10.c

P73 10.e

Variants of Quantified Conditional Statements • Statement: x  D, P(x)  Q(x) • Contrapositive: x  D, ~Q(x)  ~P(x) • Converse: x  D, Q(x)  P(x) • Inverse: x  D, ~P(x)  ~Q(x) • Same logical variants apply to existentially quantified conditional statements

18 September 2008

Introduction & Propositional Logic

4

Rules of Inference for Quantified Statements Universal Modus Ponens

Universal Modus Tollens

x  D, P(x) Q(x) P(a) aD  Q(a) Universal Instantiation

x  D, P(x) aD  P(a) 18 September 2008

x  D, P(x) Q(x) ~Q(a) aD  ~P(a) Existential Generalization

P(c) cD  x  D, P(x) Predicate Calculus

5

Errors in Decution • Existential Modus Ponens - Doesn't exist • Existential Modus Tollens - Doesn't exist

Inverse Error

xD, P(x)  Q(x) ~P(a)  ~Q(a) • Converse Error: xD, P(x)  Q(x) Q(a) P(a)

Concept • Variants of Quantified Conditional Statements • Rules of Inference for Quantified Statements