lecture notes10

# Otherwiseitisunsatisable examplenotvalidbutsatisable

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: g “x is  mortal.”  Specify the  domain as all people.    The two premises are:    The conclusion is:    Later we will show how to prove that the conclusion  follows from the premises.  Equivalences in Predicate Logic    Statements involving predicates and quantiﬁers are  logically equivalent if and only if they have the same  truth value     for every predicate substituted into these statements  and     for every domain of discourse used for the variables in  the expressions.     The notation S ≡T indicates that S and T are logically equivalent.   Example: ∀x ¬¬S(x) ≡ ∀x S(x)  Thinking about Quan*ﬁers as  Conjunc*ons and Disjunc*ons    If the domain is ﬁnite, a universally quantiﬁed proposition is  equivalent to a conjunction of propositions without quantiﬁers  and an existentially quantiﬁed proposition is equivalent to  a  disjunction of propositions without quantiﬁers.     If U consists of the integers 1,2, and 3:    Even if the domains are inﬁnite, you can still think of the  quantiﬁers in this fashion, but the equivalent expressions  without quantiﬁers will be inﬁnitely long.  Nega*ng Quan*ﬁed Expressions    Consider ∀x J(x)  “Every student in your class has taken a course in Java.”   Here J(x)  is “x has taken a course in calculus” and    the domain is students in your class.     Negating the original statement gives “It is not the  case that every student in your class has taken Java.”  This implies that “There is...
View Full Document

## This document was uploaded on 03/06/2014 for the course MATH 320 at CSU Northridge.

Ask a homework question - tutors are online