Problem Set 8
Section 6.1
#4 Show that the sequence {an} is a solution of the recurrence relation an = -3an-1 + 4an-2 if
a) an = 0:
b) an = 1:
c) an = (-4)n:
d) an = 2(-4)n+3:
#14 An employee joined a company in 1999 with a starting salary of $50,000. Every year this employee receives a raise of $1000 plus 5% of the salary of the previous year.
a) Set up a recurrence relation for the salary of this employee n years after 1999:
b) What is the salary of this employee in 2007?
c) Find an explicit formula for the salary of this employee n years after 1999:
Section 6.5
#8: In a survey of 270 college students, it is found that 64 like brussels sprouts, 94 like broccoli, 58 like cauliflower, 26 like both brussels sprouts and broccoli, 28 like both brussels sprouts and cauliflower, 22 like both broccoli and cauliflower, and 14 like all three vegetables. How many of the 270 students do not like any of these vegetables?
#10: Find the number of positive integers not exceeding 100 that are not divisible by 5 or by 7
#16: How many elements are in the union of four sets if each of the sets has 100 elements, each pair of sets shares 50 elements, each three of the sets share 25 elements, and there are 5 elements in all four sets?
Section 7.1
#4: Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a,b) Î R if and only if:
a) a is taller than b
b) a and b were born on the same day
c) a has the same first name as b
d) a and b have a common grandparent
#30: Let R be the relation {(1,2), (1,3), (2,3), (2,4), (3,1)} and
let S be the relation {(2,1), (3,1), (3,2), (4,2)} Find S o R
Section 7.3
#4 List the ordered pairs in the relations on {1,2,3,4} corresponding to the matrices (where the rows and columns correspond to the integers in increasing order):
a)
b)
c)
#14 Let R1 and R2 be relations on a set A represented by the matrices
MR1 = MR2 =
Find the matrices that represent:
a) R1 È R2 b) R1 Ç R2 c) R2 ° R1 d) R1 ° R1
Discrete Computational Structures Spring 2006
Sheller Page 1
discretes06ps8 - work