This preview shows page 1. Sign up to view the full content.
Unformatted text preview: (a) I am going to go crazy if I see another logical expression. (b) Studying for exams will not be helpful unless you get enough sleep. (c) Everyone in your class has a cellular phone. (d) Nobody in your class has a satellite phone. (e) There is a person in your class who cannot swim. (f) All students in your class can solve quadratic equations. 5. Establish these logical equivalences, where A is a proposition not involving any quantiﬁers. • ( ∀ xP ( x )) ∨ A ≡ ∀ x ( P ( x ) ∨ A ) • ( ∃ xP ( x )) ∨ A ≡ ∃ x ( P ( x ) ∨ A ) 6. Determine the truth value of these statements if the universe of discourse for all variables consists of all real numbers. Explain. • ∀ x ∃ y ( x 2 = y ) • ∃ x ∀ y ( xy = 0) • ∃ x ∃ y ( x + 2 y = 2 ∧ 2 x + 4 y = 5)...
View Full Document
This note was uploaded on 10/03/2010 for the course MATH 240 taught by Professor Szabo during the Spring '08 term at McGill.
- Spring '08