Math 220 - 902
Final Exam Solutions
May 11, 2005
1. (20) Write the negation of the following statement:
n N (m N ) (p N ) such that mn np N .
The negation of this statement is
n N such that (m N ) (p
Math 220 - 901
1.
Final Exam Solutions
(15) Let A be a set and R a relation on A. That is, R A A.
a. Define what it means to say that R is an equivalence relation.
R is an equivalence relation if it s
Math 220 - 502
Solutions Exam 2
November 5, 2004
1. (30) Let f : N N , where N is the set of natural numbers cfw_1, 2, . Suppose that
f (n) = n2 + 1.
(a) If f injective (one-to-one)?
Yes f is injectiv
Math 220 - 901
1.
(15) Define the following terms:
a. f : X
Y,
This denotes a function from X to Y. That is a subset of X
conditions are true:
f
for all x X there is a y Y such that x, y
if x, y 1 and
Math 220 - 502
Solutions Exam 1
October 1, 2004
1. (15) Dene the following terms:
(a) If A and B are two sets, what does A B mean?
A B means that A is a subset of B . That is, if x A, then x B .
(b) I
Math 220 - 901
1.
Exam 1 Solutions
February 25, 2008
(10) Write a statement that is logically equivalent to the conditional statement P Q, using only "and
", "or
" and "negation". Be sure to prove tha
Math 220 - 502
Final Exam Solutions
May 12, 2004
1. (20) Let A, B , and C denote three sets. Prove or disprove the following:
(a) (A B ) C = (A C ) (B C )
This is a true statement. To see this Ill sho
May 7, 1997
Math 220
Final Exam
A yes or no answer or an answer with no justi cation will not be acceptable. Remember to write
neatly, clearly, and in sentences.
1. 15 If n is an even integer, show th
Math 220 - 502
Exam 2 Solutions
March 31, 2004
1. (15) Dene the following:
(a) a transitive relation on a set A. Note: there are two terms that need to be dened. They
are relation and transitive.
Firs
Math 220
Solutions Exam 2
April 1, 2005
1. (20) Dene the following terms:
(a) f is a function from the set A to the set B ,
A function from a set A to a set B is a subset of A B such that
a A, b B suc
April 3, 1997
Math 220
Exam 2
A yes or no answer or an answer with no justi cation will not be acceptable. Remember to write
neatly, clearly, and in sentences.
1. 15 De ne the following terms, and giv
Math 220 - 502
Exam 1 Solutions
February 25, 2004
1. (30) Dene the following:
(a) If A and B are two sets, what is A B ?
A B = cfw_x : x A and x B
/
(b) If A and B are two sets, what is A B ?
A B = c
Math 220 - 902
Solutions to Exam 1
February 18, 2005
1. (20) Dene the following terms:
(a) Statement (in the context of logic)
A statement is a declarative sentence, which is either true or false.
(b)
Feb. 20, 1997
Math 220
Exam 1
A yes or no answer or an answer with no justi cation will not be acceptable. Remember to write
neatly, clearly, and in sentences.
1. 20 De ne the following terms and or s