Discrete Mathematics
Math 6A
Homework 6 Solution
5.2-2 We are told that p(3)=2p(x) for each x 3, but it is implied that p(1) = p(2) =
p(4) = p(5) = p(6). We also know that the sum of these six numbers must be 1. It
follows easily by algebra that p(3)=2/7
Quiz 3
Counting: 4.3, 4.4
Quiz3: April 28, 3.30-3.45 pm
Your answers should be expressed in terms of factorials and/or powers.
1) A car dealer has 20 Chevys, 20 BMWs, 20 Pontiacs and 20 Hondas.
How many customers must buy a car on a particular day to be s
Quiz April 21 2005
Sections 1.6,1.7,1.8
Quiz: Apr. 21 05: 3.30-3.45 pm
A = cfw_ x | x = e ve n
1. Consider the following sets:
B = cfw_ x |x = o d d
U = cfw_ x (t h e unive r s al s e t )
Provide the following sets using set-builder notation:
a. A U B
Quiz 4
Counting: 4.3, 4.4, 4.5
Quiz4: May 5, 3.30-3.45 pm
Your answers should be expressed in terms of factorials and/or powers.
Imagine you want to buy books from a bookstore.
The bookstore carries 20 titles, but it has 10 copies for each title.
Your bud
Quiz 5
May 5 2005
5.1, 5.2
Discrete Probability
Quiz 4: May-04 04 3.30-3.45 pm
In the following experiment we roll a fair die 5 times.
a) What is the probability of the sequence 1,2,3,4,5.
b) What is the probability that the sequence starts with a 1.
c) W
Quiz 6
3.2 3.3 3.4
Quiz 7, June 2, 3.30-3.45 pm
1. Compute the following summations:
(note the start point of the summations)
1)
2)
37
3 ( 7 )
i
i =2
111
3 n + 5
n =1
2. Prove that the following is true for all n>2 (by mathematical induction):
2
n > 2 n
Quiz 6
1.5 Methods of Proof.
Quiz 5: Th. May 26 3.30-3.45 pm
1) Give 2 rules of inference (no names, just the equations) and the tautologies
on which they are based.
2) Formulate the following arguments symbolically and determine whether
each one is valid
Quiz Th. April 14, 3.30-3.45 pm: (explain your answers)
1. Consider the following statement:
S1 ( x, y ) : ( x > 1 y < 1)
Domain : x, y real numbers
a. Is this statement a proposition ?
b. Is the following proposition true or false: xy S1 ( x, y )
c. Is t
Discrete Mathematics
Math 6A
Homework 8 Solution
3.2-2
a) 128
b) 7
c) 2
d) -256
3.2-3
a) a0=2, a1=3, a2=5, a3=9
b) a0=1, a1=4, a2=27, a3=256
c) a0=0, a1=0, a2=1, a3=1
d) a0=0, a1=1, a2=2, a3=3
3.2-13
a) 2+3+4+5+6=20
b) 1-2+4=8+16=11
c) 3+3+.+3 = 10*3 = 30
Discrete Mathematics
Math 6A
Homework 7 Solution
1.5-1 (a) addition rule
(a) simplification rule
(b) modus ponens
(c) modus tollens
(d) hypothetical syllogism
1.5-3 Let w be the proposition "Randy works hard"
Let d be the proposition "Randy is a dull boy"
Quiz 7
6.1,6.2
Quiz 8, June 9, 3.30-3.45 pm
Solve the following recurrence relation:
f n = f n 1 + 6 f n 2
f 0 = 0 ; f1 = 5
Answer, June 9, 3.30-3.45 pm
f n = 3 ( 2 )
n
n