This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Quantifiers Let P ( x ) be a statement depending on x . Then x , P ( x ) is For all x , P ( x ) is TRUE. x , P ( x ) is There exists an x such that P ( x ) is TRUE. Example. Let P ( x ) be x 2 = 2. Is x , P ( x ) TRUE or FALSE? Is x , P ( x ) TRUE or FALSE? 1 Example. Let P ( x ) be x 2 = 2. A = x , P ( x ). B = x , P ( x ). We need to specify the universe of discourse for x . 1. U of D = Q . A and B are FALSE. 2. U of D = { 2 , 2 } . A and B are TRUE. 3. U of D = R . A is FALSE, B is TRUE. 2 If U of D is P then x,y x is equivalent to y = 1. ( y is a least element in P ). y x,y x is TRUE. (There is a least element in P ). y x,y x is FALSE. (Any positive integer is least in P ). 3 Let S be some U of D. Then x S , P ( x ) means For all x from S , P ( x ) is TRUE x S , P ( x ) means There is x from S such that P ( x...
View
Full
Document
This note was uploaded on 02/05/2010 for the course MATH 135 taught by Professor Andrewchilds during the Spring '08 term at Waterloo.
 Spring '08
 ANDREWCHILDS

Click to edit the document details