Download CECS 228 Group Exercise 2 - Logic and Discrete Structures and more Assignments Discrete Structures and Graph Theory in PDF only on Docsity!
CECS 228 - Group Exercise 2 – Monday, 2/6/
(Due on Wednesday, 2/8/06)
Group Name :_____________________________________________________________________
1. Problem 24 in Section 1.2 : Show that p ( q r ) and q ( p r ) are logically equivalent by a) Using a truth table p | q | r |
| | | | | | | | | | | | | | | | | | | | | | | |
b) Applying known logical equivalences and laws 2. Problem 10 in Section 1. Define C ( x ) “ x has a cat”, D ( x ) F ( x ) where the universe of discourse for variable x consists of ______________________________. Express each of the following statements in terms of C ( x ), D ( x ), F ( x ), quantifiers, and logical connectives. continue on the other side
a) A student in your class has a cat, a dog, and a ferret. b) All students in your class have a cat, a dog, or a ferret. c) Some student in your class has a cat and a ferret, but not a dog. d) No student in your class has a cat, a dog, and a ferret. e) For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has one of these animals as a pet.
3. Problem 36 in Section 1. Translate each of the following system specifications into English where the predicate S ( x , y ) is “ x is in state y ” and where the universe of discourse for x and y consists of all systems and all possible states, respectively. a) x S ( x , open) b) x ( S ( x , malfunctioning) S ( x , diagnostic) ) c) x S ( x , open) x S ( x , diagnostic) d) x S ( x , available) e) x S ( x , working)
