Comments on this Solutions Manual

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– The quiz solutions manual quizsol.pdf.

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1

Problem Solutions – Chapter 1

Problem 1.1.1 Solution

Based on the Venn diagram on the right, the complete Gerlandas

pizza menu is

• Regular without toppings

• Regular with mushrooms

• Regular with onions

• Regular with mushrooms and onions

• Tuscan without toppings

• Tuscan with mushrooms

M O

T

Problem 1.1.2 Solution

Based on the Venn diagram on the right, the answers are mostly

fairly straightforward. The only trickiness is that a pizza is either

Tuscan (T) or Neapolitan (N) so {N, T} is a partition but they

are not depicted as a partition. Specifically, the event N is the

region of the Venn diagram outside of the “square block” of event

T. If this is clear, the questions are easy.

M O

T

(a) Since N = T

c

, N ∩ M 6= φ. Thus N and M are not mutually exclusive.

(b) Every pizza is either Neapolitan (N), or Tuscan (T). Hence N ∪ T = S so

that N and T are collectively exhaustive. Thus its also (trivially) true that

N ∪ T ∪ M = S. That is, R, T and M are also collectively exhaustive.

(c) From the Venn diagram, T and O are mutually exclusive. In words, this

means that Tuscan pizzas never have onions or pizzas with onions are never

Tuscan. As an aside, “Tuscan” is a fake pizza designation; one shouldn’t

conclude that people from Tuscany actually dislike onions.

(d) From the Venn diagram, M ∩ T and O are mutually exclusive. Thus Gerlanda’s doesn’t make Tuscan pizza with mushrooms and onions.

(e) Yes. In terms of the Venn diagram, these pizzas are in the set (T ∪ M ∪ O)

c

.