This preview shows page 1. Sign up to view the full content.
Unformatted text preview: y and z . (b) There is no smallest positive real number. (c) Every real number has a unique cubed root. 4: For each of the following statements, determine whether it is true when the universe of discourse is Z and whether it is true when the universe of discourse is R . (a) ∀ x ∃ y ( x = y × y ∨ y × y + x = 0) (b) ∀ x ∃ y ( y < x ∧ ∀ z ( z < x → z ≤ y ) ) (c) ∀ x ∀ y ( (0 < x ∧ x + y < x × y ) → < y ) 5: Prove each of the following statements, where the universe of discourse is R . (a) ∀ x (  x 24 x  ≤ x ↔ ( x = 0 ∨ (3 ≤ x ∧ x ≤ 5) )) (b) ∀ x ∀ y ( y 2 = x 3 + x 2 ↔ ∃ z ( x = z 21 ∧ y = z 3z ) )...
View
Full
Document
This note was uploaded on 07/25/2011 for the course MATH 135 taught by Professor Andrewchilds during the Spring '08 term at Waterloo.
 Spring '08
 ANDREWCHILDS
 Algebra

Click to edit the document details