Prob.

$q < 5000$ 组询问，问 $x$ 是否可以表示为 $\sum_i a_is_i, a_i \ge 0$.

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Answers to Problems from Logic: A Very Short Introduction

VSI 这套好书迟早被这些译者毁了。

Chapter 1

Is the following inference deductively valid, inductively valid, or neither? Why? Jose is Spanish; most Spanish people are Catholics; so Jose is Catholic.

Chapter 2

Symbolize the following inference, and evaluate its validity. Either Jones is a knave or he is a fool; but he is certainly a knave; so he is not a fool.

Chapter 3

Symbolize the following inference, and evaluate its validity. Someone either saw the shooting or heard it; so either someone saw the shooting it someone heard it.

Chapter 4

Symbolize the following inference, and evaluate its validity. Everyone wanted to win the prize; so the person who won the race wanted to win the prize.

Chapter 5

Symbolize the following inference, and evaluate its validity. You made an omelette, and you don't make an omelette and not break an egg; so you broke an egg.

Chapter 6

Symbolize the following inference, and evaluate its validity. It's impossible for pigs to fly, and it's impossible for pigs to breathe under water; so it must be the case that pigs neither fly nor breathe under water.

Chapter 7

Symbolize the following inference, and evaluate its validity. If you believe in God, then you go to church; but you go to church; so you believe in God.

Chapter 8

Symbolize the following inference, and evaluate its validity. It has always rained, and it always will rain; so it's raining now.

Chapter 9

Symbolize the following inference, and evaluate its validity. *Pat is a woman, and the person who cleaned the windows is not a woman; so Pat is not the person who cleaned the windows.

Chapter 10

Symbolize the following inference, and evaluate its validity, where the level of acceptability is 0.5. Jenny is clever; and either Jenny is not clever or she is beautiful; so Jenny is beautiful.

Chapter 11

The following set of statistics was collected from ten people (called 1-10).

$$\begin{matrix} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\ \hline \text{Tall} & v & & v & & v & & & & v & \\\\ \text{Wealthy} & v & & v & & v & & v & v & & \\\\ \text{happy} & v & v & & v & v & & & v & v & \\\\ \end{matrix}$$

If r is a randomly chosen person in this collection, assess the inductive validity of the following inference. r is tall and rich; so r is happy.

Chapter 12

Suppose there are two illnesses, A and B, that have exactly the same observable symptoms. 90% of those who present with the symptoms have illness A; the other 10% have illness B. Suppose, also, that there is a pathology test t distinguish between A and B. The test gives the correct answer 9 times out of 10.

1. What is the probability that the test, when applied to a randomly chosen person with the symptoms, will say that they have illness B?
2. What is the probability that someone with the symptoms has illness B, given that the test says that they do?

Chapter 13

You hire a car. If you do not take out insurance, and you have an accident, it will cost you $1,500. If you take out insurance, and have an accident, it will cost you$300.

The insurance costs \$90, and you estimate that the probability of an accident is 0.05. Assuming that the only considerations are financial ones, should you take out the insurance?