Discrete Structures
HW #9 —
§2.2: Set Operations
Last Update: 7 November 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 #9"
AT TOP RIGHT OF EACH PAGE;
STAPLE MULTIPLE PAGES 
 (3 points each, total = 12 points)
p. 130: 4 a–d
 You are given 2 sets and asked to compute their union,
intersection, and set differences.

(3 points)
p. 130: 14
 You are given the intersection and set differences of two
sets and asked to compute what the two sets are.
 Suggestion: Use a Venn diagram to help you picture the
sets.
 (3 points each; total = 6 points)
p. 131: 16 a, b
 You are asked to prove two set equalities concerning union
and
intersection.
 (3 points)
p. 131: 24
 You are asked to prove a set equality concerning set
difference.
 Suggestion: This is easiest to prove by using the
fact that S –T = S ∩ (‾T),
along with the Distributive Law (p. 124, Table 1).
 Hint: Start by expressing the righthand side of the
equation in terms of ∩ and ‾ .
 (3 points each; total = 6 points)
 Read the definition on p. 131, column 2, of the
symmetric difference of two sets. Then express this
definition in the language of firstorder predicate logic plus
set theory;
i.e., find a predicate P such that
A ⊕ B =def {x  P(x)}.

Do p. 131: 32.
 (6 points each; total = 12 points)
p. 131, #48 a, b
 You are asked to find the infinite unions and intersections
of two sequences of sets.

Hint: Compute A_{1}, A_{2}, A_{3},
A_{4}, …, to see what patterns you can find that might
help you compute the answers.

For full credit, you must show your work, not just your answers.
Total points = 42
Tentative grading scheme:
A 4142
A 3840
B+ 3637
B 3435
B 3133
C+ 2930
C 2428
C 2023
D+ 1519
D 814
F 0 7
DUE: AT THE BEGINNING OF LECTURE, FRI., NOV. 12 
Text copyright © 2010 by William J. Rapaport
(rapaport@buffalo.edu)
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