note to
yourself
of due date
|
section |
number |
comment |
|
Getting started
|
| Day 1 |
|
|
In the textbook, read
the Preface to the student and
Section 1.1.
Since the textbook has not arrived for several
of you, here is scanned copies of:
Preface to the student
,
Section 1.1
,
Answers to selected exercises from section 1.1 (from back of book)
.
Of course, you will have to get a book but I will provide scans
of the first section material for those of you whose books did
not arrive in time.
|
|
§ 1.1 :
Propositions and Connectives
|
| |
1.1 |
1 aefh |
Obviously, in this problem you need to explain your answer. |
| |
1.1 |
2 abde |
Obviously, in this problem you need to explain your answer. |
| |
1.1 |
3 fgj |
|
| |
1.1 |
6 bh |
Show the propositional forms are equivalent via a
truth table and an explanation of how the truth table
tells you so. |
| |
1.1 |
9 ab |
Explain how your truth table gives you your answer. |
| |
1.1 |
10a |
Explain your answer. |
| |
1.1 |
11 bdf |
|
| |
1.1 |
12 c |
|
| |
1.1 |
|
Not to hand in but rather to help study for the exam.
Starred problems from: 1, 2, 3, 6, 9, 10, 11. |
|
§ 1.2 :
Conditionals and Biconditionals
|
| | 1.2 |
1 bcegh
|
Try doing without looking at IS 1.2.4.
|
| | 1.2 |
2 bcegh
|
|
| | 1.2 |
3 ALL
|
Explain your answer: a truth table along with some verbage will do.
|
| | 1.2 |
5 bdfgh
|
Explain your answer.
|
| | 1.2 |
6 befij
|
Explain your answer.
|
| | 1.2 |
7 ade
|
|
| | 1.2 |
10 bcfgjk
|
Glaze over the solutions to the starred problems before starting
the assigned problems as so to better understand the instructions.
|
| | 1.2 |
12 c
|
Show the propositional forms are equivalent via a
truth table and an explanation of how the truth table
tells you so.
|
| | 1.2 |
13 bd
|
Explain your answer:
a truth table along with some verbage will do.
|
| | 1.2 |
14 abcd
|
Explain your answer:
a truth table along with some verbage will do.
|
| | 1.2 |
16 bj
|
Explain how your truth table gives you your answer.
|
| |
1.2 |
|
Not to hand in but rather to help study for the exam.
Starred problems from:
1, 2, 5, 6, 7, 10, 12, 13, 16.
|
|
§ 1.3 :
Quantifiers
|
| | 1.3 |
1 bdkm
|
Glaze over the solutions to the starred problems before starting
the assigned problems as so to better understand the instructions.
|
| | 1.3 |
2 bdkm
|
Glaze over the solutions to the starred problems before starting
the assigned problems as so to better understand the instructions.
|
| | 1.3 |
3 ALL
|
Of course, you have already read the
Preface to the Student in the textbook.
Where on the IS can you find this info?
Be careful of the difference between the
natural numbers and the integers.
|
| | 1.3 |
6 bcd
|
Explain your answer.
|
| | 1.3 |
7 a
|
Follow example of the related proof (of the denial of "for all") from
class
notes.
|
| | 1.3 |
8 beij
|
Explain your answer!
|
| | 1.3 |
9 acf
|
Do I need to say again?
Glaze over the solutions to the starred problems before starting
the assigned problems as so to better understand the instructions.
|
| | 1.3 |
10 bcegj
|
Do I need to say it again?
Explain your answer !!!
|
| | 1.3 |
12 bcd
|
Some helpful
class
notes.
|
| | 1.3 |
14
|
|
| |
1.3 |
|
Not to hand in but rather to help study for the exam.
Starred problems from:
1, 2, 6, 8, 9, 10, 13.
|
|
§ 1.4 :
Basic Proof Methods I
|
| | 1.4 |
5abceg,
7hjkl,
8a,
9acd,
10bc,
11be.
|
-
On problems 5-10, also write symbolically, using quantifiers (as we did in class).
-
17 problems * 10 pts/problem so this assigment is worth 170 pts
|
| |
1.4 |
|
Not to hand in but rather to help study for the exam.
Starred problems from: 5, 7, 10, 11
|
|
§ 1.5 :
Basic Proof Methods II
|
| | 1.5 |
3cfh,
4c,
5ac,
6cde,
7acd,
9,
10,
12acd.
|
-
For each problem, also write symbolically, using quantifiers (as we did in class).
-
17 problems * 10 pts/problem so this assigment is worth 170 pts
|
| |
1.5 |
|
Not to hand in but rather to help study for the exam.
Starred problems from: 3, 4, 6, 12.
|
|
§ 1.6 :
Proofs Involving Quantifiers
|
| |
1.6 |
3,
4b,
4c,
6e,
6d,
7g.
|
-
For each problem,
write the problem symbolically, using quantifiers.
-
For 7g (proof to grade), the book gives a proof
by contradiction. Grade the book's proof.
Then also write a direct proof
(the contrapositive will come in handy for this).
-
6 problems * 10 pts/problem so this assignment is
worth 60 points.
|
| |
1.6 |
|
Not to hand in but rather to help study for the exam.
Starred problems from:
|
|
§ 1.7 :
Additional Examples of Proofs
|
| |
1.7 |
2e,
4a,
4c,
7b.
|
-
For each problem,
write the problem symbolically, using quantifiers.
-
Hint for 2e. By the Division Algorithm for the
integers Z,
n ∈ N⊂ Z so (take d=3)
for some q∈ Z and r ∈ {0, 1, 2}
we have n=3q+r. (Tbe bold face N and Z are like the
N and Z I make on the chalkboard with "extra lines" but I don't
know how to make them like this for the web.)
-
Hint for 4c. You can use 4a to show 4c.
-
4 problems * 10 pts/problem so this assignment is
worth 40 points.
|
| |
1.7 |
|
Not to hand in but rather to help study for the exam.
Starred problems from:
|
|
§ 2.4 :
Principle of Math Induction (basic form and generalized form)
|
|
§ 2.5 :
Principle of Math Induction (generalized form)
|