Math 3.1
Weekly Summary, Week 3, Chapter 3, Discrete Mathematics Name:
Due on Sunday, September 16, by midnight.
Type your answers under the questions given below, or, print out this sheet, use pen or pencil to fill it out, and email a scan or photo of it to the instructor.
1) In your own words, explain Russell's Paradox, which is outlined in section 3.1, problem #27. What I am looking for here is a basic explanation, of around 5 ( 10 sentences, that is accessible to any student who understands section 3.1.
2) Suppose we look at the list of binomial coefficients:
÷
÷
ø
ö
ç
ç
è
æ
0
n
,÷
÷
ø
ö
ç
ç
è
æ
1
n
,÷
÷
ø
ö
ç
ç
è
æ
2
n
,…,÷
÷
ø
ö
ç
ç
è
æ
n
n
.a) If n is an even number, which binomial coefficient is the largest?
b) If n is an odd number, which two binomial coefficients are the largest? [Hint: take a look at Pascal's triangle.]
3) Here we will add to the list of the Laws of Set Theory. In the most reduced form possible, what do each of the following sets equal?
a) A ( A =
b) A (
A
=c) U ( A =
d) A ( U =
e) A (
A
=f) If A ( B then A ( B =
4) Let S be a set with |S| = 10. Let the elements of set S1 be all two element subsets of S. Let the elements of set S2 be all two element subsets of S1. Which is larger, |P(S)| or |S2| ?
[Note: P(S) is the power set of the set S.]
5) If four dice (of different colors) are rolled, what is the probability that their sum equals 6? Show all of your work.
bonus: Suppose that A ( B, B and C are disjoint, |B ( A| = 1502, |A| + |C| = 510, |
C
| = 1606, and |B
| = 414. What is |U| ?