Solution of Homework 2: Language of Mathematics
Q1. Prove
AB =AB
without using the De Morgans law and Venns Diagram.
Answer
To prove that two sets are equal, we need to prove that each set is a subset
CS182 Spring 2013 Homework 7
Prof. Alex Pothen and Prof. Vernon Rego
Due date: Friday April 26, 2013
(LE1: Before Class; LE2: 9 A.M. in CS undergrad oce).
Late HW will not be accepted.
1. (10 points)
[50] Homework 4. Proof Techniques
Each problem is worth 10 points
[10] Show that
3
3 is irrational.
[10] Show that 3 divides n3 + 2n whenever n is a nonnegative integer.
[10] Let A be a set of cardina
CS182 Spring 2013 Homework 3
Prof. Alex Pothen and Vernon Rego
Due date: Friday, February 22, 2013 (before class).
1. (4pts) Find these terms of the sequence cfw_an , where an = (2)n + 5n.
(a) a0 .
(b
CS 182 Fall 2010
Michael S. Kirkpatrick
Name:
MIDTERM #1
This is an open book, open notes exam. However, you are not allowed to share any
material with anyone else during the exam. Any evidence of aca
Solution of Homework 3
* Note that the approximate functions shown below are not unique and
are provided for the sake of illustration not perfection.
Prob. 1
n
n!
e
Using Stirlings formula:
n
n
2n
CS 182 Fall 2009
Prof. Ananth Grama
Final Exam
Answer Key
PROBLEM 1
Let P (x, y ) be the statement x-y = x+y. The domain for both variables is the set of all
integers Z. What are the truth values of t
[30] Homework 3. Programming Assignment
The goal of this assignment is to find good approximations of
(2) Hn
=
1 k2 k=1
n
and n! = 1 2 3 n for large n (n ). [15] Evaluation of (Zeta Functio
CS182 Spring 2013 Homework 1
Prof. Alex Pothen and Vernon Rego
Due date: Friday, January 25th, 2013 (before class).
1. (8pts) Show that each of these implications is a tautology by using truth tables.
[50] Homework 2. Language of Mathematics Each problem is worth 10 points [10] Prove that for any sets A and B A = (A - B) (A B). [10] Let x and y be integers. Determine whether the following relatio
Purdue University Vernon J .Rego
West Lafayette Fall 2017
CS 182
Assignment 5
Due: Wednesday, November 15th, 2017, upload before 11:59pm
1) (15 pts.) Answer the following:
a. Prove or disprove: For al
Wig
PROBLEM 1): Logic
[6](A). State the converse of statement (a), the contrapositive of (b) and the inverse of (C)-
(a) If it snows tonight, then I will stay at home.
/7 / 9% W6 may, ,4 ,2/ field
lmy
Purdue University Vernon J .Rego
West Lafayette Fall 2017
CS 182
Assignment 4
Due: Wednesday, November 1st, 2017, upload before 11:59pm
1) (50 pts.) Solve the recurrences:
a) an=4an_1
ao=1
Vn > 1
b) a
Purdue University Vernon J .Rego
West Lafayette Fall 2017
CS 182
Assignment 3
Due: Wednesday, October 4th, 2017, upload before 11:59pm
1) (20 pts.) Do Exercise 52 of Section 3.1 (page 204)
2) (20 pts.
Purdue University Vernon J .Rego
West Lafayette Fall 2017
CS 182
Assignment 6
Due: Sunday, December 3rd, 2017, upload before 11:59pm
P.S: Few more questions will be added next week. Also, the assignme
Purdue University Vernon J .Rego
West Lafayette Fall 2017
CS 18200
Assignment 1
Due: Wednesday, September 6, 2017, upload before 11:59pm
1) (30 pts.): Do Exercise 32 from Chapter 1.1 (Page 15)
(15 pts
CS 18200
Study
Guide
Table of Contents
Break Up Problem-wise for the final
Chapter 1: Logic and Proofs
Propositions
Truth Tables
Equivalences/DeMorgans Laws
Predicates and Quantifiers
Nested Quantifie
Your Name:
CS 182
Midterm Solutions
Spring 2017
Left Neighbor:
Right Neighbor:
This exam contains 9 numbered pages. Check your copy and exchange it immediately if
it is defective. Print your name and
Things to Know.
Existential Quantifier:
There exists an x such that P (x) is true.
Universal Quantifier:
(x)P (x)
For all x, P (x) is true.
Binomial Coefficient:
(x)P (x)
The number of m-combinations
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Purdue University
West Lafayette
CS 182
Vernon J.Rego
Fall 2017
Assignment 5
Due: Wednesday, November 15th, 2017, upload before 11:59pm
1) (15 pts.) Answer the following:
a. Prove or disprove: For all
1) (20 pts.) Do Exercise 52 of Section 3.1 (page 204)
(I will use Q as quarters, D as dime, N as nickels, and P as pennies.)
a) 87 cents.
Q: 3; D: 1; P: 2.
b) 49 cents.
Q: 1; D: 2; P: 4.
c) 99 cents.
Purdue University
West Lafayette
CS 182
Vernon J.Rego
Fall 2017
Finals Cheat Sheet
1) Inference rules:
2) The formula for
n
k
=
n!
k!(nk)!
3) Combination formula :
C(n,k)= number of ways of choosing k