Last Update: 20 March 2009
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Reminder: Each HW problem solution should consist of:

- a restatement of the entire problem (you may copy it word for word),
- followed by a complete solution with all intermediate steps shown.

All exercises are from §2.2 (set operations).

- (3 points each; total = 12 points)
Let A = {a, b, c, d, e} and B = {a, e, i, o, u}. Find

- A ∪ B
- A ∩ B
- A – B
- B – A

- (6 points each; total = 12 points)
(This is problem 16d, e on p. 131.)

Let A, B be sets. Prove each of the following, justifying each step.- A ∩ (B – A) = ∅
- A ∪ (B – A) = A ∪ B

- (3 points each; total = 6 points)
Let A, B be sets.

Then**the symmetric difference of**A**and**B (denoted A ⊕ B) =_{def}the set containing those elements in either A or B, but not in both A and B.- 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*)}. - Find {a, c, e} ⊕ {a, b, c}.

- Express this definition in the language of first-order
predicate
logic plus set theory;
- (3 points each, total = 12 points; for full credit, you must show
your work, not just your answer.)
**Hint:**Compute A_{0}, A_{1}, A_{2}, A_{3}, …, to see what patterns you can find that might help you compute the answers.Find ∪

_{i ∈ N}A_{i}and ∩_{i ∈ N}A_{i}, if, for every*i*∈**N**,- A
_{i}= {*i*, 2*i*, 3*i*, …}. - A
_{i}= {*i*,*i*^{2},*i*^{3}, …}

- A

Total points = 42.

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 BEGINNING OF LECTURE, FRIDAY, MARCH 27 |

Copyright © 2009 by William J. Rapaport (rapaport@cse.buffalo.edu)

http://www.cse.buffalo.edu/~rapaport/191/S09/hw08.html-20090317-2