Welcome to the Course Page of

MATH 1190 3.00 B

Introduction to Sets and Logic

Fall 2015


Department of Mathematics and Statistics
Faculty of Science
York University
4700 Keele Street
Toronto, Ontario  M3J 1P3

Course Organization:


Course Information

Course Schedule


Exams Information

Links & Other Resources


This area will contain announcements and solutions to tests. Announcements made in class will be posted here in reverse chronological order and will not be repeated in class. Please take a minute to read the announcements carefully, as they often get updated. You may need to Reload/Refresh this page.

December 28:

Please  click here  to see your final exam mark and unofficial


letter grade for the course. Please also note that your official


grade for the course will be available by the Registrar's


Office upon the faculty approval.


Happy Holidays!

December 02:

Please note that the Final Examination for the course will take place on


Thursday, December 17, 2015 from 19:00 to 22:00 in TC AVIVA.


The exam will be comprehensive, covering the entire course material


covered in class according to the Course Schedule with an emphasis on


the more resent material covered after Test #2.


There will be several questions, some with a few parts. Marks for each


question will be indicated. You have to show all your work and should


explain your solutions where appropriate. Unofficial final grades for the


course will hopefully be posted to the course web page by January 3, 2016.


I am making available a copy of the final examination for the course from


the Winter Term of 2012 (courtesy of Prof. E. Brettler).

December 01:

Please note that the graded Test #3 papers will be returned in the class on


Thursday, December 03. I am making available a scanned copy of solutions


to the test questions in PDF format.

November 22:

According to your requests, I am making available solutions to Test #2,


Test #3 and Test #4 with solutions in PDF format from the Winter Term of


2012 (courtesy of Prof. E. Brettler).

November 19:

As is was announced in the class today, on Test #3 you will also be responsible


for the material covered in class from Section 2.5 of the textbook.

November 18:

Please note that we will write Test #3 on Thursday, November 26, 2015 from


7:00 to 8:10 PM in two class-rooms as follows:


- family name starting with A - K: CLH H (please note the change from Test #2);


family name starting with - Z: CLH K.


On the test you will be responsible for all the material covered in class from


Sections 2.3, 2.4, 2.5, 4.1, 4.2, 4.3, 4.4, 4.5 and 4.6 of the textbook.

November 16:

Please note that the student course evaluations are available at the URL link:


http://courseevaluations.yorku.cafrom November 16th to December 8th, 2015.


It is the time for you to be the judge. Please go on-line and complete the course


evaluation. Thank you!

November 11:

Practice exercises for Chapters 4, 5 and 9:


Section 4.1: 1, 5, 6, 7, 8, 9, 10, 13, 16, 21, 22, 24, 25, 26, 28, 29, 30, 35;


Section 4.2: 1, 2, 3, 4, 6, 10, 12, 21ab, 22;


Section 4.3: 1, 2, 3, 4, 5, 8, 15, 17, 24, 25, 26, 30, 33, 39de, 52;


Section 4.4: 3, 5, 9, 11, 21, 31;


Section 5.1: 3, 4, 5, 6, 7, 8, 10, 11, 16, 18, 19, 21, 28, 33, 34, 40, 48, 50, 55;


Section 5.2: 2, 4, 14, 22, 26, 30, 40;


Section 5.3: 1, 3, 25;


Section 9.1: 1, 2, 3, 4, 5, 6, 7, 8, 16, 20, 24, 34, 40, 41, 48, 56;


Section 9.5: 1, 2, 3, 7, 8, 9, 10, 12, 15, 16, 22, 30, 36, 44, 45, 47, 48, 52, 55, 56, 62.

November 04:

Please note that the graded Test #2 papers will be returned in the class on


Thursday, November 05. I am making available a scanned copy of solutions


to the test questions in PDF format.

October 16:

As it was announced in the class yesterday, we will write Test #2 on Thursday,


October 22, 2015 from 7:00 to 8:10 PM in two class-rooms as follows:


- family name starting with A - L: CLH H;


family name starting with - Z: CLH K.


On the test you will be responsible for all the material covered in class from


Sections 1.5, 1.6, 1.7, 1.8, 2.1 and 2.2 of the textbook.

October 14:

Please note that the graded test papers will be returned in the class on


Thursday, October 15.


Practice exercises for Chapter 2:


Section 2.1: 1, 2, 3, 6, 7, 8, 9, 10, 14, 18, 20, 21, 28, 32, 35, 38, 42;


Section 2.2: 2, 3, 4, 12, 13, 15, 19, 20, 23, 27, 28, 29, 30, 36, 40, 48, 52;


Section 2.3: 2, 3, 4, 5, 7, 8, 10, 11, 12, 14, 15, 16, 18, 21, 22, 30, 32, 36, 38, 40, 54, 58, 72;


Section 2.4: 3, 5, 6, 9, 10, 14, 18, 20, 25, 26, 32, 33, 34, 42;


Section 2.5: 1, 2, 3, 4, 6, 10, 16, 22, 23, 28.

October 07:

I am making available a scanned copy of solutions to Test #1 questions


in PDF format. Please note that the graded test papers will hopefully be


returned in the class on Thursday, October 15.

October 02:

Practice exercises for Sections 1.6-1.8:


Section 1.6: # 2, 3, 6, 7, 10, 15, 16, 20, 24, 30, 35;


Section 1.7: # 1, 2, 3, 6, 7, 8, 9, 12, 18, 23, 24, 26, 31, 32, 36, 39, 42;


Section 1.8: # 1, 3, 9, 17, 19.


Review Questions (page 111): 1-16.

September 27:

Please note that starting Thursday, October 01, Tutorials for the course


will take place in CLH K.

September 25:

As it was announced in the class yesterday, we will write Test #1 on Thursday,


October 01, 2015 from 7:00 to 8:00 PM in two class-rooms as follows:


- family name starting with A - L: CLH H;


- family name starting with M - Z: CLH K.


On the test you will be responsible for all the material covered in class from


Sections 1.1, 1.2, 1.3 and 1.4 of the textbook.


You may click here to see Test #1 with solutions in PDF format from the Winter


Term of 2012 (courtesy of Prof. E. Brettler).

September 18:

As it was announced in the class yesterday, Tutorials for the course will be on


Thursdays from 18:00 to 18:50. Please note that until further announcement the


tutorials will take place in N501 Ross.


I am also making available the weekly schedule of the Math Lab for Fall Term.

September 10:


To view and/or print  PDF  files you need to download the Acrobat Reader  http://www.math.yorku.ca/~raguimov/math1505c_y13/getacro.gif


Practice exercises for Sections 1.1-1.5:


Section 1.1: # 1, 2, 5, 6, 7, 8, 9, 11, 13, 14, 16, 17, 19, 20, 21, 22, 23, 27, 28, 31, 34, 35, 37, 38, 43;


Section 1.3: # 3, 5, 6, 7, 8, 9, 10, 11, 12, 17, 23, 24, 25, 31, 34, 42, 44, 46, 58;


Section 1.4: # 3, 6, 7, 8, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 26, 31, 32, 35, 36, 42, 44, 47, 49, 58, 59, 62;


Section 1.5: # 2, 3, 7, 10, 11, 14, 20, 24, 25, 27, 31, 32, 39, 40, 45; 46, 50.


If you would like to be a class representative for this course, please see me during the


break today. To read the letter from the Bethune College Masterís Office please click


the link. Some additional information can be found on the following Bethune College


CR Program webpage: bethune.yorku.ca/classreps/

Course Information


Term and Session:

Fall 2015

MATH 1190





R 19:00-21:50, CLH H



Dr. Iouldouz Raguimov



S512 Ross



416-736-2100, Ext. 66092 or 416-736-5250


Office Hours:

T 16:00-17:30, W 12:00Ė13:30, also by appointment






R 18:00-18:50, CLH K

Tutorial Leader:


Mr. Muqiao Huang





Three Tests:

20% each


Final Examination:



Course Description: This course is program requirement in Computer Science. It is also intended for math majors and other students wanting an introduction to discrete mathematics. The topics covered are basics of propositional and predicate logics, proof techniques, sets, functions, relations, modular arithmetic and applications of elementary number theory, induction. The emphasis will be on understanding the basic concepts, mathematical reasoning, proofs and problem solving that will be required in upper level MATH courses. For a more detailed list of topics with references to the textbook, please see Course Schedule.

Textbook and

Discrete Mathematics and Its Applications, Seventh Edition

other aids:

by Kenneth H. Rosen


McGraw-Hill, 2012. ISBN: 798-0-07-338309-5.

Optional Aids:

Studentís Solutions Guide for Discrete Mathematics and Its Applications, Seventh Edition


by Kenneth H. Rosen


McGraw-Hill, 2012. ISBN: 798-0-07-735350-6.


Please see www.mhhe.com/rosen for more information regarding the textbook.

Reference Sources:

There are a number of copies of the book in the Steacie Science Library


in two-hour reserve.

Course Prerequisites:

At least one 12U or OAC mathematics course or equivalent.

Course Credit

GL/SCLA/MATH/MODR 1650 3.00, SC/MATH 1019 3.00.


Important Dates:

September 10: Classes commence.


September 24: The last date to enrol in the course without my permission.


October 08: The last date to enrol in the course with my permission.

October 29-November 01: Fall Reading Days (no classes).


November 09: The last date to drop the course without receiving a final grade.

December 07: The last date to submit term work.


December 07: Classes end.


December 08: Study day.


December 09-23: Examination period.

Course Schedule

(Tentative, subject to any changes announced in class)




Sept 10

Introduction, 1.1

Classes begin on Thursday, September 10.

Sept 17


Sept 24


September 24 is the last day to enrol without my permission.

Oct 01


Test #1 will take place on Thursday, October 01. 

Oct 8

1.8, 2.1

Oct 15


Oct 22

2.4, 2.5

Test #2 will take place on Thursday, October 22. 

Oct 29

No classes

Fall Reading Days.

Nov 05


Nov 12



Nov 19



Nov 26


Test #3 will take place on Thursday, November 26. 

Dec 03

9.5, Review

Classes end on Thursday, December 03.

Dec 09-23

Final Examination


Note: The course will not cover all the sections of each chapter of the textbook.


Throughout the term, practice exercises will be posted to the Announcements section. In order to develop your understanding of the course material you must do all assigned problems. These will not be collected for grading and hence, will not directly affect your grade. However, it is extremely important that you complete as many exercises as possible. Do not memorize them. Rather, learn how to solve problems like them. Learning Mathematics is not a spectacular sport, it is a participatory event. There is nothing like a bit of computation to strengthen understanding in mathematics! Use the Solutions Manual only after you have tried the problem. Successful students must keep up with homework and seek help for points they do not understand as soon as possible. Do not fall behind! For excellent success and understanding in this course, it is recommended that you read the relevant sections of the textbook ahead of each class. Next to the classes, working out the answers to the problems is the most important preparation for the tests and exam that will contain for the most part but not exclusively, questions very similar to those from the textbook. It is quite practical to work on your own or together in small groups. Each student should do at least three hours of independent study for every lecture hour. The amount you learn in this course and the grade you receive will be proportional to the amount of time you spend working on problems.
Note: Help is also available in the Math Lab in S525 Ross.

Exams Information

Lecture/Exam Rules:

All internet connected and other distractive electronic devices (cell phones, pagers, head phones, digital dictionaries, CD players, laptops) need to be turned off and kept out of sight by all participants during class, i.e. during lectures, tutorials, tests and exams. All such devices as well as all books, papers, knapsacks, and briefcases must be left at the front of a lecture hall during tests and exams. Anyone caught with electronic devices will be charged with Academic Dishonesty (see the next page). The only items you may have at your seat during exams and tests are pens, pencils, eraser, student ID and purses. Notes need to be taken manually; use of cellphone cameras in class is not allowed. Activities (such as newspaper reading, food consumption) that are not conducive to maintaining an atmosphere of attention and learning in class ought to be avoided. You are responsible for all material covered in lectures.
Note: Photo identification and signing-in are required at all tests and exams. No calculators will be permitted.

Final Grade:

The official grades at York University are LETTER grades. Qualitative descriptions of these grades can be found in the York Calendar at this link. Your test marks will be on a numerical scale because these have to be weighted and averaged in various ways, but THERE IS NO AUTOMATIC PREDETERMINED CORRELATION BETWEEN NUMERICAL GRADES AND LETTER GRADES in this course. In particular, the "numerical" grades you receive are NOT to be interpreted as percentages; they are merely 'raw scores'. When the tests are returned in class, the distribution of 'raw scores' will be announced along with an approximate conversion to letter grades. The median letter grade for the course will likely fall between D+ and C+.
The composition of the final grade is as follows:
Three Tests (60 minutes each written tests held in lecture periods): 20% each (Tentative dates for the tests: Thursdays, October 01, October 22 and November 26, 2012);
Final Examination 
(three-hour exam scheduled by the Registar's Office): 40% of the overall grade, will take place in December 2015, during the examination period.
Students have five days from the date of the return of test papers to appeal their marks. Some test papers (randomly selected) are photocopied before they are handed back, so we can detect subsequent alterations.

Make-up Policy:

No permission will be given to a student to write tests in advance of their scheduled dates. No make-up will be done for the tests. A missed test will be counted as zero, except under extreme circumstances in which case the corresponding percentage of the overall grade will be "forwarded" to the final exam. If you miss a test for medical reasons, you must turn in within one week following the test date the Attending Physician's Statement form provided here after getting it filled in by your doctor. No other type of medical note will be accepted. However, missing tests is extremely dangerous and not recommended. As experience has shown, students who miss class tests because of some 'mysterious illnesses' will usually average 30% on the final exam.
Student who misses the final examination will be allowed to write a make-up exam only if both of the following conditions are met:
the student notifies me (raguimov@mathstat.yorku.ca) or the Department of Mathematics and Statistics (Undergraduate Office, N502/503 Ross Building, 416-736-2100, Ext. 55902 or 33969) in advance that the exam will be missed;
the student submits within one week following the exam date the Attending Physician's Statement form provided here after getting it filled in by his/her doctor.
Students who miss the final examination and do not meet both conditions will receive a grade of F. It is student's responsibility to fill out and submit the Deferred Standing Agreement form.
Note: Do not make vacation/job plan until the final exam date is known: having a plane ticket for Banff or Hawaii on December 15 is NOT a legitimate excuse for absence from a final exam on December 18.

Religious Observance and Accessibility:

Special needs students please identify yourself to the course instructor as soon as possible. York University is committed to respecting the religious beliefs and practices of all members of the community and making accommodations for observances of special significance to adherents. If any of the dates specified in the course schedule for in-class tests pose such a conflict, students should contact me (raguimov@mathstat.yorku.ca) within the first two weeks of classes. Please note that if the final exam date poses a conflict, students must complete the Final Exam Accommodation form, which can be obtained from the Registrarís Office. Please note that York University welcomes feedback on accessibility issues. Your feedback may be provided by sending e-mail to: mathstat@yorku.ca

Academic Honesty:

Students are responsible for familiarizing themselves with University Policies and Regulations. Conduct that violates the ethical or legal standards of the university community or of oneís programme or specialization may result in serious consequences. Refer to the Senate Policy on Academic Honesty. Photo identification and signing-in are required at all tests and exams. Also, some test papers (randomly selected) will be photocopied before they are returned so that subsequent alterations can be detected.


Individual questions can be discussed by e-mail or in person after class, or during office hours. Please send all e-mail notes as plain text within the body of the message. Do not send attachments or HTML-formatted e-mail. No texting, please. Also, if the name of your account is an alias, I will not know who the mail is from unless you sign it; it also risks being accidentally discarded as junk mail. The course web page will be up-dated regularly to include important announcements made in class, such as the material to be covered on the tests. E-mail notes requesting such information contained on the web page will be answered the last.

Links and Other Resources

1-York Undergraduate Math Program
2-Infinity Club
3-Online Forum
4-Local time in Toronto

Questions and comments regarding this web page please send to raguimov@mathstat.yorku.ca

© 2004-2015, All Rights Reserved, York University & Iouldouz S. Raguimov

Last updated December 28, 2015