cs245-asn5

cs245-asn5 - valid. If they are valid, demonstrate their...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 245 Winter 2009 Assignment 5 Due: Thu 12 Mar 2009 10am in the CS245 Drop Boxes 35 marks You must submit your assignment with a cover page produced using makeCover , otherwise you will lose 2 marks. Assignments are to be completed individually. The policy on academic ofenses is on the course web page. 1. (9 marks) Formalize the ±ollowing sentences in set theory. Do not use types, quanti²ers, or set comprehension. Use only the ±ollowing sets and relations in your ±ormulas: Dwellings – the set o± dwelling People – the set o± people Houses – the set o± houses Students – the set o± students owns : People Dwellings The relationship between people and the dwellings that they own. rents : People Dwellings The relationship between people and the dwellings that they rent. where Students People , Houses Dwellings . Sentences to ±ormalize: (a) All houses that are rented are owned. (b) Not every student owns a house. (c) Students who rent houses do not own any dwelling. 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. (26 marks) Determine whether the following arguments in set theory are valid or in-
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: valid. If they are valid, demonstrate their validity. You may use natural deduction or trans-formational proof. In both types of proofs, you may use the axioms and derived laws of set theory. If you use natural deduction, do not use any logical laws from transfor-mational proof. In transformational proof, you may use the logical laws of predicate and propositional logic. If the argument is invalid, provide a counterexample and demonstrate that the argu-ment is invalid. (a) R ( | C | ) R ( | C | ) = B where R : A B,C A (b) ran(((( R D ) C ); id Y ) ) = dom( R ( C D )) where R : X Y,C Y,D Y (c) ( B R ) ( A R ) = ( B A ) R where R : X Y,A X,B X (d) ( y ( x,y ) ( R S )) ( y ( x,y ) ( R S )) where R,S : X Y ( x is a constant.)...
View Full Document

Page1 / 2

cs245-asn5 - valid. If they are valid, demonstrate their...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online