Name
Homework #4
Fundamentals of Advanced Mathematics 3450:307 Dr. Norfolk
1. Determine which of the following are statements, and give the truth value.
(a) Is it raining outside now?
(b) February 14 is Valentines Day
(c) This sentence is false
(d) Add th
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Name
Dr. Norfolk
Final Examination (take-home)
Show your work.
Fundamentals of Advanced Mathematics 3450:307
Due: Wednesday, May 6, 2009, 10:00am
1. Let cfw_xn be a sequence of real numbers. Recall that lim xn = L if and only if, given any
n
>
Name
Homework #5
Fundamentals of Advanced Mathematics 3450:307 Dr. Norfolk
Prove the following, by the basic method indicated:
1. (Trivial) Let x IR. If 0 < x < 1, then x2 2x + 2 = 0.
2. (Vacuous) Let n IN. If |n 1| + |n + 1| 1, then |n2 1| 4.
3. (Direct
Name
Homework #3
Fundamentals of Advanced Mathematics 3450:307 Dr. Norfolk
1. Let A = cfw_1, 2, 3, 4. How many possible partitions of A exist?
2. Let B = cfw_1, 2, 3, 4, 5, 6 Find partitions S of B for which
(a) |S | = 3
(b) cfw_5 S
3. Let C = cfw_a, b. L
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Name
Test 1
Fundamentals of Advanced Mathematics 3450:307 Dr. Norfolk
July 13th, 2000
Show your work.
1. Construct the complete truth table for the propositional form
P Q Q R
10 points
2. Find the values (if possible) of P and Q for which the f
Name
Homework #2
Fundamentals of Advanced Mathematics 3450:307 Dr. Norfolk
1. Sketch the most general Venn diagram for three sets A, B, C , and shade the region
(a) (C B ) A
(b) C (A B )
2. Give an example of sets A, B, C which are intervals, and for whic
Name
Homework #8
Fundamentals of Advanced Mathematics 3450:307 Dr. Norfolk
1. Disprove: If n cfw_1, 2, 3, 4, 5, then 3 | (2n2 + 1).
2. Prove by contradiction: If x is irrational and r is a non-zero rational, then rx is irrational.
3. If x > 0 and x
2
> 1
Name
Homework #1
Fundamentals of Advanced Mathematics 3450:307 Dr. Norfolk
1. Let A = cfw_a, cfw_b, c, cfw_c. Determine whether the following are true or false.
(a) b A
(b) cfw_a A
(c) a A
(d) cfw_a A
(e) c A.
2. (a) Write B = cfw_n Z : n2 < 8 in roster f
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Name
Test 3 (take home)
Summer 2011
Show your work.
Fundamentals of Advanced Mathematics 3450:307
Dr. Norfolk
1. Let P denote the set of all people alive on August 1, 2011, and B be the set of all books
written before that day.
Dene a relation
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Name
Test 2
Fundamentals of Advanced Mathematics 3450:307
Summer 2011
Show your work.
Dr. Norfolk
1. Disprove: (x IR Q )(y IR Q )(x + y IR Q ).
Q
Q
Q
10 points
2. Grade the following proof, and explain your reasoning:
A - completely correct, if
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Name
Test 2
Fundamentals of Advanced Mathematics 3450:307
April 20, 2009
Show your work.
Dr. Norfolk
1. (a) Claim: For sets A, B, C ,
A (B C ) = (A B ) (A C )
Find a counterexample to this claim.
10 points
(b) Prove the following: If A, B are s
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Name
Test 1
Fundamentals of Advanced Mathematics 3450:307
Feb 25, 2009
Show your work.
Dr. Norfolk
1. Construct the complete truth table for the propositional form: P R Q R
P
QR
10 points
2. Suppose that P Q is false. Evaluate:
(a) (P Q) Q
5 po
Test Total
Name
Test 1
Fundamentals of Advanced Mathematics 3450:307
Summer 2011
Show your work.
Dr. Norfolk
1. Draw the most general Venn diagram for sets A, B, C , and shade the region which represents
(C A) B .
5 points
2. List the elements of A = cfw_
Name
Homework #6
Fundamentals of Advanced Mathematics 3450:307 Dr. Norfolk
Prove the following, for integers a, b:
1. If a|b, then a2 |b2 .
2. If a|b and b|a, then a = b.
3. If 3| and 3| then 3|(a2 b2 ).
/a
/b,
4. 3|(2a2 + 1) i 3|
/a.
Name
Homework #7
Fundamentals of Advanced Mathematics 3450:307 Dr. Norfolk
1. Prove that, if n is odd, then n2 1 mod 8.
2. Prove that, if r IR and 0 < r < 1, then
1
4.
r(1 r)
What happens if we change the domain of discussion to Z
Z?
3. Prove that, for s