This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: PRACTICE FINAL 1. True or False? (2 pts each) L is a firstorder language (with equality). M and M are interpretations of L . X M is the domain of M . X M is the domain of M . ( x ) is a formula in L that has x as its only free variable. [ x : t ] is obtained from by replacing every free occurrence of x by t . If X M has more elements than X M and X M is finite, then there is a L such that M  = and M  = . If A and B are Ldefinable subsets of X M , then A B is an Ldefinable subset of X M X M . If M  = x ( x ), then X M is the subset of X M that is defined by ( x ). If M  = x x , then M  = x ( ). If a and b are constant symbols in L and M  = [ x : a ] [ x : b ] for all , where has x as its only free variable, then M  = a b . 2. Explain (5 pts each) Explain two of your answers from Section 1. 3. Inductive Definition (5 pts each) Using the successor function, give an inductive definition of the set { ( q,r,s )  q,r,s N and q + r s } . Show that your set contains (2 , 1 , 3). 4. Evaluate Sentences (2 pts each) Let L be contain three binary relation symbols: R 1 , R 2 , and R 3 . Let M be the following interpretation of L : X M = { (...
View Full
Document
 Spring '11
 H

Click to edit the document details