Here you will see info about what we did in class, upcoming exams, solutions for past exams, etc.,

Started 8/16/2017

Starting August 30th, all section and problem numbers are from 8th edition


Review problems for test (Please ALSO review homework problems AND class notes):
Chapter I self test:
(8th edition)1,2,3,4,5,6,8,12,13,14,15,16,17,18,19,22,23,24.
(7th edition) All except problems 9 to 18.
Chapter II self test:
(8th edition): All upto 16.
(7th edition): All except problems from 2.3.

You can also try these old exams:
Our exam will be similar in format but some problems will be on topics different from those in these exams.
Fall 04 Test I (all except 4b and 5)
Fall 06 Test I (all except 7)

Tuesday, 9/19/2017
I have uploaded some old exams of mine. See above
Our exam will be similar in format but some problems will be on topics different from those in these exams.

Monday, 9/18/2017
Today we did problems using proof by strong induction.
Please look at review problems for test posted above
HW3 can be submitted wednesday by 4pm.
Please try the following problems from 2.4 and 2.5 for practice.
They don't need to be submitted.
2.4: (8th ed.) 1,5,13,19,22,28,45; (7th ed.) 1,5,12,18,21,27,42
2.5: (8th ed.) 1,7,10 ; (7th ed.) 1,6,11.
Please study this paper by Kei Nakamura to learn about Fibonacci numbers and using induction to prove their properties.

Friday, 9/15/2017
Today we did more problems using proof by induction.
Please look at review problems for test posted above
HW3 can be submitted wednesday by 4pm.

Wednesday, 9/13/2017
Today we talked about proofs by cases and started proof by induction.
No new HW problems but I encourage you to try as many problems from book on induction as possible.
Problem 2.4.17 (2.4.16 in 7th ed.) is quite interesting and slightly more challenging.

Monday, 9/11/2017
Today we talked about methods of proofs, including proof by contradiction and by example.
HW3 (total 10 problems; due on or before monday 5pm in office):
Problems 7 to 10: 8th edition: 2.2: 33,38,48,52.
7th edition: 2.2: 28,33,43,47.
If anyone needs 6th edition problems, email me.

Friday, 9/1/2017
Today we talked about Proofs and methods of proofs, including direct proof, proof by contradiction and by contrapositive.
Notes from today's class.

HW3 (more to be given monday):
8th edition: 2.1: 12,19,34 ; 2.2: 3,21,28.
7th edition: 2.1: 12,17, 32; 2.2: 3,18,23.
If anyone needs 6th edition problems, email me.

Wednesday, 9/6/2017
Today we talked about hw2.
There are 10 problems below. Please work on them asap.
Stop by my office if you need help.
They should be presented by 5pm next wed, 8/13.

Friday, 9/1/2017
Today we talked about Nested Quantifiers.
Updated and edited notes from today's class.
It also includes solution to problem 66 in section 1.1 (sets).
HW2 problems (we will discuss hw2 on wednesday).
Please try them over the break.
Section 1 (Sets : 1.1 in 7th, 2.1 in 6th ed.)
1.1.56: Draw a Venn diagram and shade the region representing B∩(C∪A)' where the second set is the complement of C∪A.
1.1.67: (see notes from today for example problem) In a group of students each is taking a math or computer course or both. 1/5th of those taking a math course are also taking computer, and 1/8th of those taking a computer course also taking math. Are more than 1/3rd taking a math course?
Section 1.6 (Nested Quantifiers ; 1.4 in 6th ed, 1.6 in 7th).
1.6.35: Let L(x,y) be the function "x loves y." If P is set of all living people then domain of discourse is P x P. Write the statement "Everybody loves somebody" symbolically.
1.6.50: Determine the truth value of ∃x∀y(x^2 < y+1) if domain of discourse is R x R.
1.6.73: Given domain of discourse is R x R x R determine whether the following statement is true or false: ∀x∃y∃z ((x < y) →((z > x)∧(z < y)).

Wednesday, 8/30/2017
Today we talked about Quantifiers. Notes from today's class.
HW2 problems (more will be added friday):
Section 1 (Sets / specifically section on Cartesian products)
1.1.73: If X = {1,2}, Y = {a}, Z = {α, β} list the elements of X x Y x Y.
1.1.79: Give a geometric description of ZxZ.
Section 5 (Quantifiers)
1.5.29: Write ∃x(Not(P(x)) using only negation, AND and OR symbols given that D = {1,2,3,4}
1.5.41: Given that D = {people}, P(x) is " x is a professional athlete" and Q(x) is "x plays soccer" determine the truth value of ∀x(Q(x) → P(x)) and write it in words.
1.5.49: Given that D = {people}, P(x) is " x is an accountant" and Q(x) is "x owns a Porsche" write"Some accountant owns a Porsche" symbolically.

Monday, 8/28/2017
Today we mainly went over the homework I that is due by friday.
Please come to my office any day this week between 2 and 3pm with completed hw.

Friday, 8/25/2017
Today we talked about Basic logical statements and De Morgan's law.
Please read the following Notes from today's class. I have included more details including answers for the questions.
Please note that the section numbers below are for 6th edition of textbook.
The order of the sections are a bit scrambled in the newer editions.
I hope to have the latest edition soon.
Also I did not cover Truth tables in class because they are quite easy.
Please read and use truth tables when necessary (indicated in problem below).
Also read definitions of converse, sufficient condition and necessary condition.
Homework problems from 1.2 for today (will discuss some of the HW on monday):
Write the following statements as conditional propositions. Also write their converses, contrapositives:
1.2.3: A necessary condition for Fernando to get a computer is that he gets 2000 dollars.
1.2.6: The audience will go to sleep if the chairperson lectures.
1.2.44: Using truth tables, check whether the following are logically equivalent: The statements "p -> q" and "(Not p) OR q"

Wednesday, 8/23/2017
Homework 1 problems: (more will be added friday)
1.1, 3. Write the negation of "For some positive integer n, 19340 = 17n"
1.1, 17 (Given p is F, q is T, r is F, is the statement (NOT(p OR q))AND(NOT(p) OR r) true?)
1.1, 51: Write symbolically: You did not hear "Flying pigs" rock concert (p is F) and you did not hear Y2K concert (q is F) but you have sore eardrums (r is T).

Monday, 8/21/2017
Notes from today's class
Please read the following to get started on the course:
Note on Russell's paradox
This note contains its definition, history, an example using web search principles, and the Barber of Seville example. I compiled it from various web-sites