Power Set P(s) all subsets inside of a set; has 2n subsets
Example: Scfw_0, 1, 2 : P(cfw_0, 1, 2) = cfw_ , cfw_0, cfw_1, cfw_2, cfw_0,1, cfw_0,2, cfw_1,2, cfw_0,1,2 Scfw_ : P(cfw_) = cfw_ , cfw_
For Acfw_ cfw_a, cfw_a,cfw_b , A, A, cfw_a A cfw_a A, cfw_
(cse260)
Homework 2 Solutions
September 24, 2015
Note: the last problem (1 point) is to give the number of hours you used to do this homework. Keep
recording the time from now.
Total points (131 points)
1: [1.5.7]. Let T(x; y) mean that student x likes cu
Sec 1.5
6.
p: it rains
r: the sailing race is held
t: the trophy will be awarded
H1: ( p q) ( r s)
H3: t
1.
2.
3.
4.
5.
6.
7.
8.
q: it is foggy
s: lifesaving demonstration will go on
H2: r t
p
t
Hypothesis H3
rt
Hypothesis H2
r
Modus tollens using (1) and
CSE260
Solutions to Homework Set #5
1. List the members of these sets.
a) cfw_x | x is a real number such that x = 1
cfw_-1, 1
b) cfw_x | x is a positive integer less than 12
cfw_1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
c) cfw_x | x is the square of an integer a
CSE260
Solutions to Homework Set #1
2. Which of these are propositions? What are the truth values of those that are propositions?
a) Do not pass go.
This is not a proposition; it's a command.
b) What time is it?
This is not a proposition; it's a question.
(7
l
r
. 3 f.) x (L
v
l "2 ; v
\2/ a} 65) 1 315m" 1 Mk Sma Q66 1° 55.an SmmP", HUI)» At S'Ud SKEW-1'
63 V m3 Evm CM m Xihek mmw. Dru: Wm) aaum * S'Lgni 63.1th
B {(105th RH Um: pang: \m'X'v. a-umw'vum sun-.1
4 gnu. \Jdo PUK-l) £2. 3mm \gemnc (I (3'53 h 4
Exam 1, Form ee CSE 260, Michigan State University Fall 2014
(1) (20 points) For each assertion below, indicate if it is true (T) or false (F) by
circling the correct response. N denotes the set of natural numbers and W is the
set of all positive natural
Quiz 1a, CSE 260, Fall 2013
1
Name:
To receive full credit, you must write legibly and your answers must be clear. There are 4 problems
(front and back). (Maximum: 20 pts.)
1. (6 pts) Construct the truth table for the formula p (q r).
p
q
r
p
qr
p (q r)
F
Quiz 2a, CSE 260, Fall 2013
Name:
1
To receive full credit, you must write legibly and your answers must be clear. There are 4 problems
(front and back). (Maximum: 20 pts.)
1. (6 pts) Sets.
(a) What is |cfw_ , cfw_ x , cfw_ y , cfw_ x, y |?
4
(b) Is cfw_
Quiz 2b, CSE 260, Fall 2013
Name:
1
To receive full credit, you must write legibly and your answers must be clear. There are 4 problems
(front and back). (Maximum: 20 pts.)
1. (6 pts) Sets.
(a) Is cfw_ a cfw_ , cfw_ a , cfw_ b , cfw_ a, b ?
Yes.
(b) Is
Quiz 3a, CSE 260, Fall 2013
Name:
1
To receive full credit, you must write legibly and your answers must be clear. There are 4 problems
(front and back). (Maximum: 20 pts.)
1. (7 points) Find the following values:
(a) 39 mod 12
3 (since 39 = 3 12 + 3 and
Quiz 3b, CSE 260, Fall 2013
Name:
1
To receive full credit, you must write legibly and your answers must be clear. There are 4 problems
(front and back). (Maximum: 20 pts.)
1. (7 points) Find the following values:
(a) 49 mod 11
5 (since 49 = 4 11 + 5 and
Quiz 4a, CSE 260, Fall 2013
Name:
1
To receive full credit, you must write legibly, your answers must be clear, and you must (briey!)
explain your reasoning. There are 4 problems (front and back). (Maximum: 20 pts.)
1. What is the minimum number of cards
Quiz 4b, CSE 260, Fall 2013
Name:
1
To receive full credit, you must write legibly, your answers must be clear, and you must (briey!)
explain your reasoning. There are 4 problems (front and back). (Maximum: 20 pts.)
1. If A and B are nite sets with |A| =
Exam 3, Form A
CSE 260
Fall 2012
Name:
Section:
Date:
INSTRUCTIONS:
(1) DO NOT OPEN YOUR EXAM BOOKLET UNTIL YOU HAVE BEEN TOLD
TO BEGIN.
(2) This exam booklet contains 13 questions. The total points for the exam is 150
points. The number of points possibl
CSE 260
Discrete Structures in Computer Science
Fall 2013
http:/www.cse.msu.edu/~cse260
Instructor: Dr. Laura Dillon
Office Hours: 3132 EB Mon & Wed noon 1:30 p.m., and by appt.
Email: ldillon@cse.msu.edu (preferred method of contact)
Phone: 517-353-4387
é
' \OO
/ Quiz 3. Form CE CSE 260 Fall 2014
0
Name: .
Section: L Date: ll 2 [(111
INSTRUCTIONS:
Closed book. 20 minutes. To receive full credit, you must write legibly and your answers
must be clear. There are 3 problems. (Maximum: 100 points.)
(1) (35 po
Exam 2, Form EF
CSE 260 Fall 2014
\E/J) (
) (20 points) For each assertion below, indicate if it is true (T) or false (F) by
circling the correct response. R , Q, Z and N denote the set of real numbers,
ratio 1 numbers, integers, and natural numbers,
(CSE260)
Homework 6 Solutions
November 2, 2015
For all proof question rubrics +2 for trying, +3 correctness.
1: [2.4.35]. Show that
numbers (5 points)
Pn
j=1 (aj
aj1 = an a0 ), where a0 , , an is sequence of real
Solution:
n
n
n
X
X
X
rCl
(aj aj1 ) =
aj