Discrete Structures
HW #8 —
§2.1: Sets
Last Update: 29 October 2010
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All exercises come from, or are based on exercises from, the Rosen text.
Each HW problem's solution should consist of:
All solutions must be handwritten.
PUT YOUR NAME, DATE, RECITATION SECTION, &
"HW #8"
AT TOP RIGHT OF EACH PAGE;
STAPLE MULTIPLE PAGES 
 (3 points each; total = 18 points)
p. 120: 6 a–f
 You are asked whether {2} is a member of various sets.
 For full credit, you must give a correct reason
justifying each answer.
 I strongly urge you to do p. 120, #5, first.
 (3 points each; total = 18 points)
p. 120: 8 a–f
 You are asked whether certain sets are members or proper
subsets of various sets.
 For full credit, you must give a correct reason
justifying each answer.
 I strongly urge you to do p. 120, #7, first.
 (3 points)
p. 120: 16
 This question concers the relation between ∈ and
⊆
 Note: More than one answer is possible.
 (3 points each; total = 12 points)
p. 120: 18 a–d
 You are asked about the cardinality of various sets,
i.e., about the number of elements that each set has.
 (3 points each; total = 12 points)
p. 120: 28 a–d
 You are asked to compute several Cartesian products.
 (3 points each; total = 6 points)
p. 121: 38 a–b
 You are asked to show why Russell's paradox is
paradoxical.
Total points = 69
Tentative grading scheme:
A 6669
A 6265
B+ 5961
B 5558
B 5154
C+ 4750
C 3946
C 3238
D+ 2431
D 1323
F 012
DUE: AT THE BEGINNING OF LECTURE, FRI., NOV. 5 
Text copyright © 2010 by William J. Rapaport
(rapaport@buffalo.edu)
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