M IDTERM EXAM INATION Nathan Redford CSC 226-002 10/14/2008
19.
If we align one set across the top of the diagram and the other down the left hand side of the diagram, we can list all cartesian prod
1. P T T T T F F F F
a. p (q r) (p q) (p r) q T T F F T T F F r T F T F T F T F q r T T T F T T T F p (q r) T T T F F F F F p q T T F F F F F F p r T F T F F F F F (p q) (p r) T T T F F F
This le contains the exercises, hints, and solutions for Chapter 2 of the book Introduction to the Design and Analysis of Algorithms, 2nd edition, by A. Levitin. The problems that might be challenging
Special Test 1
Topic: Propositional Calculus and Truth Tables
1.
p (q r )
(q s) t
(p s)
Prove t using a direct proof.
2.
pq
rs
(p s)
Prove (q r) using proof by contradiction.
Given:
Given:
p (q r )
rs
Jason Krontz 3-9-09 CSC 226 MIDTERM 1.)
p T T T T F F a.) F (q T T F F T T F b.) F
(q v r) (p q) v (p r)
T T T T T F F T T F F T T F T F F F T F F T F T F T F T T T T T T T T T T T T F F F T T T
CSC 224/226 Discrete Mathematics
First Exam Review
Write your name on all sheets.
Reasons given in proofs must include line numbers as well as rule.
Rules can be given by name or number.
THIS IS A CLO
-LOGICPropositions
A proposition is a statement that
can, in principle, be determined to
be either True (T) or False (F).
-E.g. Today is Monday
-Today is Tuesday
-The square root of 4 is 2
-The square
North Carolina State University Course Syllabus
CSC 226 - 002 - Discrete Mathematics for Computer Scientists
CSC 226 Course Syllabus
CSC 226 Discrete Mathematics for Computer Scientists
Section 002
FA
University of Washington, Tacoma TCSS 342, Winter 2006, Section B (Hong) Assignment #7 version 1.1 Due: Thursday, March 9, 2006, 4:15 PM Please show your work and explain your reasoning. Write legibly
ITCS2175 Logic and Algorithms
Third Exam Review
75 minutes
Problem
1
2
3
4
5
6
7
8
9
Total
TOPIC
Induction
Induction
Big-O
O, Omega,
Theta
Relations
Relations
Counting
Counting
Counting
Possible Point
L4.1-2
Lecture Notes: Mathematical Induction
It is often the case that we want to consider the truth of statements such as
(1)
n
i = n(n+1)/2, n0
i =0
This means that the sum from zero to any natural
About Integers:
Division algorithm:
Let a be an integer and d be a positive integer.
Then there are unique integers q and r such that
a = dq + r, 0 r<d.
7 3=2 with remainder 1: a=7, d=3, q=2, r=1.
-7
L1.5-7
Lecture Notes: Methods of Proof
All proofs are alike!
This sounds like a broad and capricious generalization but it is nonetheless
true. Any proof begins with axioms or premises, (or whatever y
Use induction to prove that if A_1,A_2, A_n are sets, then A_1^c
A_n]^c
Basis:
N= 1
A_1^c = [A_1]^c
LHS = RHS
Assume:
N
N
[A_k]^c = [
K=1
A_k]^c
k=1
Prove:
N
N
[A_k]^c = [
K=1
A_k]^c
k=1
N
=
[A_k]^c
[
15. [CSC226HW5.52 (103591)] SAVE THIS FILE ON YOUR COMPUTER. OPEN
IT WITH WORD, and SAVE IT in WORD format. UPLOAD on WebAssign.
Prove that 3 is irrational by contradiction
Note: use ^ for powers and
The article by Zenia Kish goes into depth about black culture, specifically the music they
produced, post Hurricane Katrina. The title of the article, My FEMA People: Hip-Hop as Disaster
Recovery in t
L3.5-6
Lecture Notes: Primes and Greatest Common Divisors (GCDs)
An extremely important concept is that of the prime number. Prime numbers
are to mathematics what atoms are to chemistry: the building
ITCS2175-Logic and Algorithms
Second Hour Exam REVIEW
Set Theory, Predicate Calculus, Arithmetic Proofs
Induction, Recursion
75 minutes
Write your name on all sheets.
Reasons given in proofs must incl