HKUST Department of Computer Science and Engineering
COMP 2711: Discrete Math Tools for CS Spring 2012
Midterm Examination 1
Date: Friday, March 2, 2012
Name:
Email:
Time: 19:0021:00
Student ID:
Lecture and Tutorial:
Instructions
This is a closed book ex
COMP 2711 Discrete Mathematical Tools for CS
Fall 2013 Written Assignment # 2
Distributed: Sept 18, 2013 Due: Sept 25, 2013
Your solutions should contain (i) your name, (ii) your student ID #, (ii) your
email address and (iv) your tutorial section.
Proble
The Tennis Club Problem
The Tennis Club Problem
Sort the members in some order.
Take the rst member and pair him
with any of the other 2n 1 members.
A tennis club has 2n members.
We want to pair up the members (by twos) to play
singles matches.
Take the n
COMP 2711 Discrete Mathematical Tools for CS
Fall 2013 Written Assignment # 2
Solution
Your solutions should contain (i) your name, (ii) your student ID #, (ii) your
email address and (iv) your tutorial section.
Problem 1: Consider the sets S4 = cfw_a, b,
COMP 2711 Discrete Mathematical Tools for CS
2013 Fall Semester Solution to Written Assignment # 6
Distributed: Nov 1, 2013 Due: Nov 8, 2013
At the top of your solution, please write your (i) name, (ii) student ID #, (iii)
email address and (iv) tutorial
Problem 1
Problem 1
What is the probability that a hand of 5 cards chosen from
an ordinary deck of 52 cards, will consist of cards of the same
suit?
The rst question is
What is the probability that a hand of 5 cards chosen from
an ordinary deck of 52 card
Problem 1
What is the probability that a hand of 5 cards chosen from
an ordinary deck of 52 cards, will consist of cards of the same
suit?
Problem 1
What is the probability that a hand of 5 cards chosen from
an ordinary deck of 52 cards, will consist of c
The Tennis Club Problem
A tennis club has 2n members.
We want to pair up the members (by twos) to play
singles matches.
2-1
The Tennis Club Problem
A tennis club has 2n members.
We want to pair up the members (by twos) to play
singles matches.
(a) In how
Proof of Distributive Laws
Proof of Distributive Laws
Prove the distributive laws for n multiplication over +n addition.
Prove the distributive laws for n multiplication over +n addition.
Distributive Laws said:
x n (y +n z ) = x n y +n x n z
and
(y +n z
Proof of Distributive Laws
Prove the distributive laws for n multiplication over +n addition.
5-1
Proof of Distributive Laws
Prove the distributive laws for n multiplication over +n addition.
Distributive Laws said:
x n (y +n z ) = x n y +n x n z
and
(y +
Proof by Smallest Counterexample
Proof by Smallest Counterexample
Denitions:
log2 (n) is x such that 2x = n.
log2 (n) is the unique i s.t. 2i n < 2i+1
Denitions:
log2 (n) is x such that 2x = n.
log2 (n) is the unique i s.t. 2i n < 2i+1
e.g. log2 (2) = 1
Problem 1
Problem 1
Solution:
Problem 1
Problem 1
Solution:
Problem 1
Problem 1
Solution:
Problem 1
Problem 1
Solution:
Problem 2
Problem 2
Solution:
Problem 2
Solution:
Problem 2
Solution:
Problem 2
Solution:
Problem 3
Problem 3
Solution:
Problem 4
Probl
HKUST Department of Computer Science and Engineering
COMP170: Discrete Math Tools for CS FALL 2008
Midterm Examination 2
Sketch Solution Key
Date: Tuesday , Nov 11, 2008
Name:
Email:
Time: 19:0020:30
Venues: LTA, LTC
Student ID:
Lecture and Tutorial:
Inst
Problem 1
Problem 1
Solution:
Problem 1
Problem 1
Solution:
Problem 1
Problem 1
Solution:
Problem 1
Problem 1
Solution:
Problem 2
Problem 2
Solution:
Problem 2
Solution:
Problem 2
Solution:
Problem 2
Problem 3
Solution:
Problem 3
Solution:
Problem 4
Probl
Proof by Smallest Counterexample
Denitions:
log2 (n) is x such that 2x = n.
log2 (n) is the unique i s.t. 2i n < 2i+1
e.g. log2 (2) = 1, log2 (3) = 1, log2 (4) = 2
log2 (31) = 4, log2 (32) = 5, log2 (33) = 5
1-1
Proof by Smallest Counterexample
Denitions
The problem
Consider the identity:
n
2
2-1
n2
4
=
n
4
n4
2
The problem
Consider the identity:
n2
4
n
2
=
n
4
n4
2
Example:
10
2
8
4
= 45 70
= 3150
= 210 15
10 6
=
4
2
2-2
The problem
Consider the identity:
n
2
n2
4
=
n
4
n4
2
In the next slide we will see
The problem
The problem
Consider the identity:
n
2
n2
4
Consider the identity:
=
n
4
n4
2
n2
4
n
2
=
n
4
n4
2
Example:
10
2
8
4
= 45 70
= 3150
= 210 15
10 6
=
4
2
2-1
2-2
The problem
The problem
Consider the identity:
n
2
n2
4
Consider the identity:
=
n
4
HKUST Department of Computer Science and Engineering
COMP170: Discrete Math Tools for CS Spring 2011
Midterm Examination 2
Solution Key
Name:
Email:
Student ID:
Lecture and Tutorial:
Instructions
This is a closed book exam. It consists of 14 pages and 7
HKUST Department of Computer Science and Engineering
COMP170: Discrete Math Tools for CS FALL 2008
Midterm Examination 1 Solution Sketch
Date: Thursday, October 09, 2008
Name:
Email:
Time: 19:0020:30
Venues: LT B,C,D
Student ID:
Lecture and Tutorial:
Inst
Hong Kong University of Science and Technology
COMP170: Discrete Mathematical Tools for Computer Science
Spring 2009
Midterm Exam 1
10 March 2009, 3:004:20pm, LT-E
Solutions
Question 1: Any subset of the 12 points with three or more members can be made in
HKUST Department of Computer Science and Engineering
COMP170: Discrete Math Tools for CS Spring 2010
Midterm Examination 1
Date: Thursday, March 11, 2010
Name:
Email:
Time: 19:0020:30
Venues: LT A,B,C
Student ID:
Lecture and Tutorial:
Instructions
This i
Hong Kong University of Science and Technology
COMP170: Discrete Mathematical Tools for Computer Science
Spring 2009
Midterm Exam 2
21 April 2009, 3:004:20pm, LT-E
Instructions
1. This is a closed-book exam consisting of 7 questions.
2. Please write your
Hong Kong University of Science and Technology
COMP170: Discrete Mathematical Tools for Computer Science
Spring 2009
Midterm Exam 2
21 April 2009, 3:004:20pm, LT-E
Solutions
Question 1: From the encryption step of the RSA algorithm, we know that
C = M e m
HKUST Department of Computer Science and Engineering
COMP170: Discrete Math Tools for CS FALL 2007
Midterm Examination 1 Solution Key
Date: Tue, October 09, 2007
Name:
Email:
Time: 19:0020:30
Venues: LTA, LTB
Student ID:
Lecture and Tutorial:
Instructions
HKUST Department of Computer Science and Engineering
COMP170: Discrete Math Tools for CS Spring 2011
Midterm Examination 1
Date: Friday, March 11, 2011
Name:
Email:
Time: 19:0021:00
Student ID:
Lecture and Tutorial:
Instructions
This is a closed book exa
Hong Kong University of Science and Technology
COMP170: Discrete Mathematical Tools for Computer Science
Spring 2009
Midterm Exam 1
10 March 2009, 3:004:20pm, LT-E
Instructions
1. This is a closed-book exam consisting of 6 questions.
2. Please write your
HKUST Department of Computer Science and Engineering
COMP170: Discrete Math Tools for CS FALL 2007
Midterm Examination 2
Sketch Solution Key
Date: Thursday, Nov 8, 2007
Name:
Email:
Time: 19:0020:30
Venues: LTA, LTB
Student ID:
Lecture and Tutorial:
Instr
Proof by Smallest Counterexample
Proof by Smallest Counterexample
Denitions:
log2 (n) is x such that 2x = n.
log2 (n) is the unique i s.t. 2i n < 2i+1
Denitions:
log2 (n) is x such that 2x = n.
log2 (n) is the unique i s.t. 2i n < 2i+1
e.g. log2 (2) = 1