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: SOLUTIONS TO HOMEWORK 5 MATH 150, FALL 09 Problem 1. Section 2.2/ Exercise 8. Suppose is a set of formulas such that for all sentences , either  = or  = . Assume that A  = . Show that for any , A  = iff  = . For one of the directions, suppose that  = . Then by definition of logical implication and since A  = , it follows that A  = . For the other direction, suppose that A  = . Then A 6 = . By the definiton of logical implication and since A  = , it follows that 6 = . So, by the assumptions on , we get that  = . Problem 2. Section 2.2/ Exercise 9. Assume that the language has equality and a twoplace predicate P . For each of the following find a sentence such that the model A satisfies iff the condition is met. (1) The universe of A has exactly two members. (2) P A is a function (from the universe of A to itself). (3) P A is a permutation of the universe of A (i.e. it is a onetoone, onto function). (1) = x y ( ( x = y ) z ( z = x z = y )) (2) = x y ( P ( x,y ) z ( P ( x,z ) y = z )) (3) Let f = x y ( P ( x,y ) z ( P ( x,z ) y = z )) and 11 = x y ( z...
View
Full
Document
This note was uploaded on 11/16/2009 for the course MATH 120 taught by Professor Smith during the Spring '09 term at UC Irvine.
 Spring '09
 SMITH
 Math, Formulas

Click to edit the document details