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:
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- (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 right-hand 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 first-order 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 A1, A2, A3,
A4, …, 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 41-42
A- 38-40
B+ 36-37
B 34-35
B- 31-33
C+ 29-30
C 24-28
C- 20-23
D+ 15-19
D 8-14
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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