MATH413
HW 4
due Feb 29 before class
1: How many strings of 10 English letters are there
(a) that contain x if letters can repeat?
(b) that contain a if letters cannot repeat?
(c) that contain at least one vowel if letters cannot repeat?
(d) that contain
Math 213, Exam 1 2
Question 1: (16 Points)
a) List all of the subsets of {0,{0. 1}.
¢, m, {MB}, {Mm G}
b) What is the minimum number of presidents of the United States needed to guarantee that
there are at least 50 coming from the same state? (There are c
Question 1: (16 Points)
:1) List all of the subsets of {0, {0, 1}.
¢)i{¢’ljl ipl {’16}
b) What is the minimum number of presidents of the United States needed to guarantee that
thch are at least 20 coming from the same state? (There are currently 50 state
Math 213 - Test I Preparation
Test I will include similar problems to the following. In addition to these exercises please
make sure that you read Chp. 2, Sec. 1,2,3,4,5,6, Chp. 5, Sec 1,2 and Chp. 6, Sec. 1,2. Go
through all the Homework problems and the
Professors:
Laura Escobar (lescobar at illinois)
230 Illini Hall
Office hours: Mon. 2-4, and by appointment
Jeremiah Heller (jbheller at illinois)
362 Altgeld
Office hours: Mon. 12-1, Wed. 2-3, and by appointment.
Lecture sections:
Laura Escobar: Section
Math 213: Discrete Math
Fall 2012
Midterm 2 Practice Problems November 1st, 2012
Name:
Your actual midterm will contain 8 problems; this sample contains more problems for practice purposes.
This is a closed-book, closed-notes exam. No electronic aids ar
Math 213: Discrete Math
Fall 2012
Midterm 3 Practice Problems December 3rd, 2012
Name:
This is a closed-book, closed-notes exam. No electronic aids are allowed.
Read each question carefully. Proof questions should be written out with all the
details. Ex
Math 213 — 1—Hour Exam UIN:
1. (6 points) Let A, B, C be three sets. Prove the following set identity:
(A—B)~C'§A—(B—C)
Free—Pr tor CW3 9<E (A'B)-~C , XeA~B omd X<¥C
so xeA 0ch New xeC
90 “A M We Buc
5m 8~C geuc we Woo KeA am} 2&ch
SO XeAﬁBwL) WWI/x What
Sections (Cross one):
C1 (10:00)
X1 (12:00)
G1 (15:00)
Math 213 1-Hour Exam, Fall 2012
Nov 1st, 7:00pm 8:20pm, 101 Armory, UIUC
Name (PRINTED):
UIN:
Rules and Instructions:
Please put your I-card face-up on your desk.
Write down you name and UIN on this
1. Let A, B, be sets. What is A (A B) equal to? Prove your claim.
2. Let f : A B be a function. For each of the following statements
either prove it is true or give a counterexample.
(a) f 1 (P Q) = f 1 (P ) f 1 (Q) for any pair of subsets P, Q B.
(b) f 1
1. What is the homogeneous part of the recurrence relation an = 4an1
4an2 + 2n?
2. Solve the recurrence relation an = an2 , a0 = 5, a1 = 2.
3. Solve the recurrence relation an = an1 + 6an2 , a0 = 1, a1 = 1.
4. (a) Find a recurrence relation for the numbe
Math 213, Exam 1 2
Question 1: (16 Points)
a) List all of the subsets of {0,{0. 1}.
¢, m, {MB}, {Mm G}
b) What is the minimum number of presidents of the United States needed to guarantee that
there are at least 50 coming from the same state? (There are c
Math 213, Exam 1 2
Question 1: (10 Points) What is the general solution of the recurrence relation (1n = (1,. 1 +2an_2?
Wroclmskc 0Q: r1=r+2 a (:2 Qz—I Math 213, Exam 1 3
Question 2: (10 Points) True/False. Mark each statement as either always True or som
§o|u+mns +0 odd numem rm bums.
(I) (a) No, 1814,43 :jepw :a.
(b) Veg, 5m» M+€j>ef a; Fwy = L(n-‘).£/z+4,l = h.
('5) ‘jﬂ XéCrL, n+I/1) Hm m
LX.) :n L x+ '4) :n and L’LXJ = 2n.
1; x e [ml/1W“) Hm
Lu :n , wa/LJ mm W L22d32n+L
OWE! M C(HAU‘ case m. stub LXJ+
Course Information for Math 213, Sections D1 and X1, Fall 2016
Basic Discrete Mathematics
Text: K. H. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill Inc.,
7th (or 6th) Edition, 2011; Chapters 2, 5-11 with exception of some sections
Prerequi
Math 213 / Problems for Review 1
0. Study your notes and the textbook (Sects. 2.1-2.4, 5.1-5.2, 6.1-6.5, 7.1-7.3 in the 7th edition; Sects.
2.1-2.4, 4.1-4.2, 5.1-5.5, 6.1-6.3 in the 6th edition).
1. Find the set (A B) (B C) (B A) C) if A = cfw_1, 2, . . .
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