HW #9 — §2.2: Set Operations

All solutions must be handwritten.

1. (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.

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2. 
   (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.

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3. (3 points each; total = 6 points)

   p. 131: 16 a, b

   • You are asked to prove two set equalities concerning union and intersection.

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4. (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 ‾ .

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5. (3 points each; total = 6 points)
   1. 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)}.

   2. Do p. 131: 32.

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6. (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