CS 173 Section 5 Handout, week of 10/01/07 Fall 2007
1. The first two of these are for your notes, the second two are for an exercise.
A B
U
A
C
B
U
A
C
B
U
A
C
B
U
(a) (b) (c) (d)
2. A survey of 1094 TV watchers produced the following information:
•522 watch basketball
•624 watch football
•605 watch hockey
•284 watch basketball and football
•330 watch basketball and hockey
•369 watch football and hockey
(a) What is the largest number of people who could possibly watch all 3 sports?
(b) Suppose 129 people do not watch any of the 3 sports. Exactly how many watch all 3?
3. [E&C 3.1 #11] List five elements of each of the following sets. In each case, also state which
of the sets N,Z,Q, or Rwould be an appropriate universe for the set.
(a) {2a
2b+1 |a∈Z, b ∈Z}
(b) {a2+ 1|a∈N}
(c) {ab|a∈Z+, b ∈Z}
(d) {√a2+b2|a∈N, b ∈N}
4. [E&C 3.1 #10] Write each of the following sets using a “form description” instead of a “prop-
erty description.” (For example, the property description {x∈Z|xis even}can be written
using the form description {2k|k∈Z}.)
(a) {x∈Q|x= 2mfor some m∈Z}
(b) {x∈N|xis twice a perfect square and greater than 200}
(c) {z|zis an ordered pair in the second quadrant of the Cartesian plane}
5. [E&C 3.3 #2] Prove each of the following statements about specific sets:
(a) {4m+ 1|m∈Z} ⊆ {2n−1|n∈Z}
(b) ({2n+ 1|n∈Z}∩{5m+ 4|m∈Z})⊆ {10k+ 9|k∈Z}
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