Math 318, Assignment 2
Due date: October 3, in class
Reminder: as discussed in class, below we use the notation: 0 stands
for and n = cfw_0, 1, . . . , n 1 for any positive natural number n.
1. (5 points) How many functions are there:
(1) from 2 to 3,
(2)
CLASS NOTES MATH 318
1 Propositional logic
1.1 Symbols
, ("top" and "bottom" or "true" and "false", although Loveys doesn't like the latter) propositional constants, or truth values (but don't call them that)
Propositional variables: p,q,r,q,q1,. etc
Conn
MATH 318, Syllabus for the Final Exam
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elements of set theory: sets, membership, inclusion
relations, composition of relations, transitive closure
equivalence r
MATH 318, Fall 2015
Mathematical Logic
MWF 8:359:25am, Burnside Hall 1B45
Instructor: Marcin Sabok, email: [email protected]
oce: 916 Burnside Hall, oce hours: Mondays 9:3010:30am
Course outline. The course will be divided into four parts:
(1) Eleme
ASSIGNMENT 2
COMP202, Fall 2014, All Sections
Due: October 8th , 2014 (23:59)
Please read the entire pdf before starting.
You must do this assignment individually and, unless otherwise specied, you must follow all the general
instructions and regulations
Math 104. Equivalence of Three Variations on Induction
This handout discusses three types of induction, given below, and shows that they
are equivalent. These types are:
Principle of Induction. Let P (n) be a statement (proposition) depending on a natural
Math 318, Midterm Exam
1. (2 points) Draw the following sets on R2
(1) my) 6R22x=lory=3h
(2) cfw_(m,y) E R2 : (a: > y and 932+?)2 < 1) or a: < y.
2. (2 points) Consider the following relation on the set cfw_1, 2, 3:
R = cfw_(1, 2): (2:3)'
(1) Compute the
MATH 318, Fall 2014
Mathematical Logic
MWF 8:359:25am, Burnside Hall 306
Instructor: Marcin Sabok,
email: [email protected]
office: 916 Burnside Hall,
office hours: Mondays 9:3010:30am
Course outline. The course will be divided into three parts:
(1)
MATH 318, Syllabus for the Midterm Exam
Wednesday, October 15, 2014, 8:359:25am, Burnside Hall 306
(1)
(2)
(3)
(4)
(5)
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(7)
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elements of set theory: sets, membership, inclusion
relations, composition of relations, transitive closure
equivalence
List of tautologies
Let P, Q and R be formulae, and let and be the values for "true" and "false". The following formulae1 are then
tautologies
Tautology
Explanation
P

P

PP
Reflexive law of material implication
PP

(P)P
Law of double negation
P(P)
Con
REVIEW MATH 318
Propostional Logic
1Truth tables
Given a propositional formula, write out its truth table and determine whether or not it is a tautology.
1.1General solution
A truth table for a formula of n variables will need 2n lines. Just write out eve
Math 318, Assignment 1
Due date: September 19, in class
1. (4 points) For each statement below choose if it is true or false:
(1) 1 1,
(2) 1 1,
(3) 1 cfw_1, 2,
(4) 1 cfw_1, 2
2. (2 points) Draw the following sets in R2 :
(1) cfw_(x, y) R2 : x > y + 1 and
Math 318, Assignment 4
Due date (extended): November 14, in class
1. (2 points) Let B be the LindenbaumTarski algebra with three
variables p, q, r
(1) Find all the atoms of B
(2) How many elements does B have?
2. (2 points)
(1) Does there exist an innite
Math 318, Assignment 5
Due date (extended): November 26, in class
We consider the deduction system for propositional logic (p, q, r denote below the variables) with Modus Ponens as the inference rule and
the following axiom schemes:
A1 ( )
A2 ( ( ) ( ) (
Math 318, Assignment 3
Due date: October 24, in class
1. (4 points) Write the truth tables of the following formulas:
(1) p q,
(2) (p q) (p),
(3) p (p q),
(4) q (p (q (p q).
2. (3 points) Which of the following formulas are tautologies?
(1) p (p),
(2) p (
McGILL UNIVERSITY
FACULTY OF SCIENCE
FINAL EXAMINATION
MATH 318
MATHEMATICAL LOGIC
Examiner: Professor M. Makkai Date: Monday December 17, 2007.
Associate Examiner: Professor J. Loveys Time: 9:00 A.M  12:00 PM
INSTRUCTIONS
1. Please answer questions in t
MATH 318, Assignment 3
Due date: October 17, in class
1. (4 points) Write truth tables of the following formulas. Which
of them are tautologies?
(A) (p) q,
(B) (p q) (p),
(C) p (p) q),
(D) q (p (q (p q).
2. (2 points) Devise formulas (using , and ) and sw
MATH 318, Assignment 2
Due date: October 5, in class
Suppose f : X Y is a function and A X, B Y
1. (3 points)
(1) Show that f (f 1 (B) = B.
(2) Is is always true that f 1 (f (A) = A? Justify your answer.
(3) Show that f (A f 1 (B) = f (A) B.
2. (4 points)
MATH 318, Assignment 1
Due date: September 23, in class
1. (4 points) For each statement below choose if it is true or false:
(A) 1 1,
(B) 1 1,
(C) 1 cfw_1, 2,
(D) 1 cfw_1, 2.
2. (2 points) Find all sets x satisfying
answer.
S
x = . Justify your
3. (1) (2