# Assignment #5 + Solution Winter 2009

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16 Oct 2011
School
Course
Professor
CS 245 Winter 2009
Assignment 5
Due: Thu 12 Mar 2009 10am in the CS245 Drop Boxes
35 marks
SOLUTION SET
There may be multiple correct answers to some of these questions.
1. (9 marks) Formalize the following sentences in set theory. Do not use types, quantiﬁers,
or set comprehension. Use only the following sets and relations in your formulas:
Dwellings – the set of dwelling
People – the set of people
Houses – the set of houses
Students – the set of 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.
1
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Sentences to formalize:
(a) All houses that are rented are owned.
(3 marks)
(ran rents)Houses ran owns
(b) Not every student owns a house.
(3 marks)
¬(Students dom (owns Houses))
or
dom (Students (owns Houses)) Students
(c) Students who rent houses do not own any dwelling.
(3 marks)
(dom (Students (rents Houses))) owns =
or
(dom (Students (rents Houses))) (dom owns) =
or
owns(|(dom (Students (rents Houses))) |) =
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## Document Summary

Due: thu 12 mar 2009 10am in the cs245 drop boxes. There may be multiple correct answers to some of these questions: (9 marks) formalize the following sentences in set theory. Do not use types, quanti ers, or set comprehension. 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 formalize: (a) all houses that are rented are owned. (3 marks) (ran rents) houses ran owns (b) not every student owns a house. (3 marks) 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.

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