Math 1365, 01 - Fall 2012 - Quiz 6
Name:
Use the back of the page for scratch work and initial thoughts. Only put your nal answer to be graded on
this side of the paper.
(1) 30 points. Let n k m 0 be integers. Prove the formula
choose, but write your answ
Math 1365, 01 - Fall 2012 - Quiz 4
Name:
Use the back of the page for scratch work and initial thoughts. Only put your nal answer to be graded on
this side of the paper.
(1) 50 points. Let a, b, and c be integers. Prove that if a|b, then (ac)|(bc).
(2) 50
Math 1365, 01 - Fall 2012 - Quiz 3
Name:
Use the back of the page for scratch work and initial thoughts. Only put your nal answer to be graded on
this side of the paper.
(1) Demonstrate that 2100 < 100!.
(2) Let a, b 2 Z, and dene S = cfw_x 2 Z : x|a and
Math 1365, 01 - Fall 2012 - Quiz 1
Name:
Use the back of the page for scratch work and initial thoughts. Only put your nal answer to be graded on
this side of the paper.
n
(1) A prime number p is said to be a Fermat prime if there is an integer n such tha
Math 1365, 01 - Fall 2012 - Quiz 5
Name:
Use the back of the page for scratch work and initial thoughts. Only put your nal answer to be graded on
this side of the paper.
(1) 25 points. There are n students that want to establish a club with a president an
Math 1365 - Fall 2012 - Quiz 8
Name:
Use the back of the page for scratch work and initial thoughts. Only put your nal answer to be graded on
this side of the paper.
(1) 30 points. Let s : R Z be the round-down function, which sends a real x number to the
Math 1365 - Fall 2012 - Quiz 9
Name:
Use the back of the page for scratch work and initial thoughts. Only put your nal answer to be graded on
this side of the paper.
(1) 25 points. Let A and B be a sets with |A| = 150 and |B | = 200. Give a brief justicat
Math 1365 - Fall 2012 - Quiz 7
Name:
Use the back of the page for scratch work and initial thoughts. Only put your nal answer to be graded on
this side of the paper.
(1) 30 points. Let b0 = 6, and for n > 0, let bn = 3bn1 5. Solve the recurrence relation
Math 1365, 01 - Fall 2012 - Quiz 2
Name:
Use the back of the page for scratch work and initial thoughts. Only put your nal answer to be graded on
this side of the paper.
(1) Determine whether (x) y is logically equivalent to (x (y ).
(2) Show that all six