Geometry, Fall 2012
University of Maryland, Department of Mathematics course 430
HW 2: (due by September 20, in class.)
Please write-up your own solutions to problems in an organized and neat fashion. If collaborating in the problem solving process please
Geometry, Fall 2012
University of Maryland, Department of Mathematics course 430
HW 3: (due by September 27, in class (except for problem 7see below).)
Please write-up your own solutions to problems in an organized and neat fashion. If collaborating in th
Geometry, Fall 2012
University of Maryland, Department of Mathematics course 430
HW4: (due in class October 4, in class)
Please write-up your own solutions to problems in an organized and neat fashion and staple your sheets. If collaborating in the
proble
Geometry, Fall 2012
University of Maryland, Department of Mathematics course 430
HW5: (due in class October 18)
Please write-up your own solutions to problems in an organized and neat fashion and staple your sheets. If collaborating in the
problem solving
Geometry, Fall 2012
University of Maryland, Department of Mathematics course 430
HW6: (due in class October 25)
Please write-up your own solutions to problems in an organized and neat fashion and staple your sheets. If collaborating in the
problem solving
Geometry, Fall 2012
University of Maryland, Department of Mathematics course 430
HW 1: (due by September 13, in class.)
Please write-up your own solutions to problems in an organized and neat fashion. If collaborating in the problem solving process please
Math 430: Homework 1
due: Wednesday, 9/5
(1) Let Y = cfw_Si : i I . Show: for any i I ,
Y Si .
(2) Let X be a set, and suppose S X . Show that S
X.
(3) Examples of relations:
(a) Give a binary relation on N whose domain is N.
(b) Give a function with dom
Math 430: Homework 2
due: Friday, 9/14
Exercises: Chapter 1.2, Problems 1, 3, 4, 5.
Additional exercises:
Denition 0.1. Given L0 , a nite sequence of expressions s = 1 , . . . , n is a construction sequence for if
(1) n =
(2) For all i n, either
(a) i =
Math 430: Homework 3
due: Wednesday, 9/19
Exercises: Chapter 1.2, Problems 2, 6, 8
Additional exercises:
1. Suppose , L0 are ws and let := ( ). Assume that is satisable.
Prove: if is a tautology, then is not a tautology.
1
Math 430: Homework 4
due: Wednesday, 9/26
Exercises: Chapter 1.7 Problems 5, 6.
Additional exercises: (Denitions are below the problems.)
1. Show that cfw_ is not complete.
[Hint: provide an n-place Boolean function G : cfw_T, F n cfw_T, F , for some n 1,