Questions with Set Operations, Property of Algorithms, and Pigeon Principle

1. Multiple personality disorder (MPD) is a condition in which different
personalities exist within one person and at various times control that person’s behavior. In a recent survey of people with MPD, it was reported that “98% had been emotionally abused, 89% had been physically abused, and most had experienced both types of abuse.” Make this statement more precise.

6. The owner of a corner store stocks popsicles, gum, and candy bars. After school one day, he is swamped by influx of 15 school children. They are in and out of his
store in minutes. Later, the clerk reports that ten children purchased popsicles, seven purchased gum, twelve purchased candy bars. Five purchased popsicles and gum, six purchased popsicles and candy bars, and two purchased gum and candy bars. The owner is very upset. Why?

10. A building supplies store carries metal, wood, and plastic moldings. Metal and wood molding comes in two different colors. Plastic molding comes in six different colors.
a. How many choices of molding does this store offer?
b. If each kind and each color of molding comes in four different lengths, how many choices does the consumer have in the purchase of one piece of molding?

3. Thirty buses are to be used to transport 2000 refugees from Gander to St. John’s, Newfoundland. Each bus has 80 seats. Assume one seat per passenger.
a. Prove that one of the buses will carry at least 67 passengers.
b. Prove that one of the buses will have at least 14 empty seats.

7. Determine which characteristics of an algorithm the following procedures have and which they lack.
a. procedure divide(n: positive integer) while n ≥ 0 begin
m = 1/n
n = n – 1
b. procedure chose(a, b: integers)
x = either a or b

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1. We apply the following relation between two sets A and B (involving the number of elements):
|A U B|=|A| +|B| -|A ∩ B|
Thus |AUB|=100% and |A|+|B|=98% +89%=187%
This shows that |A ∩ B|=187%-100%=87% of people had both types of abuse....