Homework Assignment

CS 171
Homework Assignment 2t
Given: January 24, 2012 Due: January 26, 2012
This assignment is due by the end of the class on the due date. Unless all problems
carry equal weight, the point value of each problem is shown in [ ]. To receive full credit all
your answers should be carefully justified. Each solution must be the student’s own work.
Assistance should be sought or accepted only from the course staff. Any violation of this
rule will be dealt with harshly.
1. Give answers to the following questions.
A. Let A = {1, 2, 3, 4, 5} and let B = {4, 5, 6, 7}. List the members of the following sets.
(a)
A B
(b) A B
(c) A B
(d) B A
(e) A × B
(f) B × A
B. State whether the following are True or False. If False then provide a counter
example.
(a)
A (B C) = (A B) C
(b) (A B) C = (A C) B
(c) (A B) C = (A C) (B C)
(d)
|A B| = |A| – |B|
(e) (A B) B = A
(f) (A B) B = A
2. John, Jim, Jay, and Jack have formed a band consisting of 4 instruments. If each of
the boys can play all 4 instruments, how many different arrangements are possible? What
if John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and
drums?

2 Homework Assignment 2t January 24, 2012
3. Answer the following questions. No justification is needed.
A. In how many ways can 3 boys and 3 girls sit in a row?
B. In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are
each to sit together?
C. In how many ways if only the boys must sit together?
D. In how many ways if no two people of the same sex are allowed to sit together?
4. Bob goes to a shop to purchase a lottery ticket. Suppose that the lottery tickets
available at that store are numbered 1
, 2, 3, . . . , 6000. Over the years Bob has found that
tickets with even numbers, tickets with numbers that are divisible by 3, and tickets with
numbers that are divisible by 5 have been unlucky for him. How many tickets have numbers
that Bob thinks are lucky for him?