hw3 - (c There is a largest integer(d There exist integers...

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

View Full Document Right Arrow Icon
Introduction to Mathematical Reasoning Fall 2009 Assignment #3: Due Wednesday, 10/21/09 Part I: 1. For each of the following statements, do the following things: Translate it into symbols. (Be sure that your symbolic statement explicitly in- cludes implied universals and domains of quanti±ers.) Negate the symbolic statement and simplify. (In particular, this means to remove parentheses in expressions of the form ( . . . ).) Translate the negated statement back into a clear and precise English sentence, without using the word “no” or “not.” (a) For every real number x , there is an integer that is greater than x . (b) There is an integer that is greater than every real number.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (c) There is a largest integer. (d) There exist integers p and q such that q > 0 and p 2 /q 2 = 2. (e) Between any integer and any larger integer, there is a real number. (f) There is an integer that is not the square of any integer. (g) Every real number has a unique cube root. (h) For every ε ∈ R + , there is a positive real number δ such that | x-2 | < δ implies | x 2-4 | < ε whenever x ∈ R . 2. Find predicates P ( x ) and Q ( x ) such that one of the following statements is true and the other is false: ∃ x ∈ R , P ( x ) ∧ Q ( x ) and ( ∃ x ∈ R , P ( x )) ∧ ( ∃ x ∈ R , Q ( x )) ....
View Full Document

This note was uploaded on 12/08/2009 for the course MATH 300 taught by Professor Staff during the Spring '08 term at University of Washington.

Ask a homework question - tutors are online