Math 511 - Set Theory

Text: Sets by W.W. Fairchild and C. Ionescu Tulcea (W.B. Saunders Company, 1970)
We will cover chapters 1-12 in the book

Links to web pages Test yourself on Venn diagrams A survey of Venn diagrams (interesting!) From Sets to Numbers If two sets of number have the same sum and the same product are they equal? Sets for teachers Set theory and transfinite numbers Sets of zeros of polynomials Set problems for high school teachers A symmetric 7 set Venn diagram (advanced)

Homework:

Jan. 21: page 5/ 1-6 and p. 14/ 1-6
Jan. 28: page 18/ 1-7
Feb. 11: First quiz and page 26/1-7
Feb. 18: Chapter 5 and Exercises 1,2,4,5,6 on page 32
Feb. 25: I originally assigned Problem p. 39/5(b) to hand in. If you are haveing trouble doing it, make up some simple examples (like let X = {a,b} and Y = {0,1} and make up some functions from X to Y and figure out what F and H are). Also we covered through chapter 8.


Download a doc file with the homework problems.
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I have also pasted them in below, but all the symbols are missing, like element signs, unin and intersection signs, etc."

Homework problems for Math 511 (March 6, 2009)

1. f:A B and g:B C are bijections. Prove that h = g f: A C is a bijection.

2. Prove that the set E = {0,2,4,6,8,…} is equipotent to the set A = {5,10,15,20,25,…}

3. Prove that the set Z (the set of integers) is equipotent to N = {0,1,2,3,4,5,…}

4. Prove that the set A = {x| x R, 0 < x < 2} is equipotent to R

5. Prove: if S is a finite set and A S then A and S-A are finite. Prove card(S) = card(A) + card (S-A)

6. Prove (by induction): if card(A) = k then card(P(A)) = 2k

7. Prove that f(k,n) = 2k(2n+1) -1 is an injection from NXN N

8. Prove (by induction) that the union of a finite number of countable sets is countable, that is , S = {1,2,…,n}, is countable if each is countable

9. Prove (by induction) that the product of a finite number of countable sets is countable, that is , S = {1,2,…,n}, is countable if each is countable

10. Let A = {1,2,3,…,k} and B = {1,2,3,…,j}. Find a bijection between

AXB and the set {1,2,3,…, kj}