Home Work 2
Submission Deadline: 10/06/2015
Problem #1
10 points
Problem #2
10 points
What will be big-Omega for Problem #1
Problem #3
10 points
Problem #4
10 points
Determine the complexity function that measures the number of print statements in an algo
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #8: Induction
Due April 13th, 2015
Answer the following questions from the textbook:
Page number Question number
329
6
329
8
330
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #9: Induction + Basic Counting Techniques
Due April 27th, 2015
Answer the following questions from the textbook:
Page number
342
344
358
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #10
Due May 11th, 2015
Answer the following questions from the textbook:
Page number
406
406
422
422
422
432
432
432
433
557
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #5: Functions
Due March 9th, 2015
Answer the following questions from the textbook:
Page number
153
153
153
154
154
155
155
153
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #2: Predicate Logic
Due February 9th, 2015
Answer the following questions from the textbook (Kenneth H. Rosen, Discrete
Mathematics and its Appli
Home Work 6
Student: Hanjie Shao
ID: N12875228
Problem 1 (10 points):
Suppose you have five coins three are good, but two are counterfeit. Assume that a counterfeit coin is
heavier than a good coin and that the two heavy coins have the same weight. A bala
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #7: Order of Growth
Due March 30th, 2015
Question 1
Rank the following functions by order of growth; that is, find an arrangement
g1, g2, g16 of
Tree
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
a connected graph which doesnt contain
simple circuit.
rooted tree: a tree in which one vertex has
been designated as the root and every edge is
directed away from the root. m
n n-1
m
N L=(N-1)/M L=[(M-1)N+1]/M
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #1: Propositional Logic
Due February 2nd, 2015
Answer the following questions from the textbook (Kenneth H. Rosen, Discrete
Mathematics and its A
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #6: Relations
Due March 23rd, 2015
Read pages 618-620 in the textbook (up to example 8 including this example),
and answer the following question
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #4: Sets
Due March 2nd, 2015
Answer the following questions from the textbook:
Page number
125
125
136
136
136
137
137
126
126
Home Work 7
Deadline: 12/6/2015
Boolean Algebra
Problem 1-3 (30 points)
Exercise 11-13 Page 844 (textbook - by Rosen)
Problem 4 (10 points)
Using Quine McCluskey method simplify the circuit for f(w,x,y,z)= (0,4,5,7,8,11,12,15)
Counting
Problem 1 (5 points
Home Work 1
Submission deadline: 09/18/2015
Problem #1
5 points
The following proposition uses the English connective or. Determine from the context whether
or is intended to be used in the inclusive or exclusive sense.
If you do not wear a shirt or do no
Home Work 4
Student: Hanjie Shao
ID: N12875228
Problem #1
for n 2, and use the Principle of Mathematical Induction to prove that the formula is correct
Answer:
Assume the formula is
n+1
2n
Basic Step:
P(2) is true because P(2) =
2+1
22
=
3
4
= (1 -
1
22
)
Home Work 5
Student: Hanjie Shao
ID: N12875228
Problem #1 (3 points)
Let A be the set of all points in the plane with the origin removed. That is,
A = cfw_(x, y) | x, y R cfw_(0, 0).
Define a relation R on A by the rule:
(a, b)R(c, d) (a, b) and (c, d) li
Home Work 7
Student: Hanjie Shao
ID: N12875228
Boolean Algebra
Problem 1
a) Explain how K-maps can be used to simplify sum-of products expansions in four Boolean variables.
b) Use a K-map to simplify the sum-of-products expansion:
Answer:
a) K-map p
Name:
CS 6003: Foundation of Computer Science
Quiz 4
ID: .
Q.1.
Time: 1 hour 25 mins
State two drawbacks of Karnaugh map. A circuit is to be built that takes the numbers 0 through 9 as
inputs (1 = 0001, 2 = 0010, . . . , 9 = 1001). Let F(w, x, y, z) be t
NYU, Polytechnic School of Engineering
CS6033: Foundations of Computer Science Spring 2015, Itay Tal
Homework #3: Rules of Inference, Proof Methods
Due February 23th, 2015
Read pages 92-96 in the textbook, and answer the following questions:
Page number
Foundations of Computer Science
Solution to Homework IV
13 November 2015
Question 1 Let A be the set of all points in the plane with the origin removed.
That is, A = cfw_(x, y)|x, y R cfw_(0, 0).
Dene a relation R on A by the rule:
(a, b)R(c, d) (a, b) an