HW #8 — §2.1: Sets

All solutions must be handwritten.

1. (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.

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2. (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.

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3. (3 points)

   p. 120: 16

   • This question concers the relation between ∈ and ⊆
   • Note: More than one answer is possible.

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4. (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.

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5. (3 points each; total = 12 points)

   p. 120: 28 a–d

   • You are asked to compute several Cartesian products.

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6. (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       66-69
A-      62-65
B+      59-61
B       55-58
B-      51-54
C+      47-50
C       39-46
C-      32-38
D+      24-31
D       13-23
F        0-12