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Chapter 1: 39E (page 24)

Freedonia has fifty senators. Each senator is either honest or corrupt. Suppose you know that at least one of the Freedonian senators is honest and that, given any two Freedonian senators, at least one is corrupt. Based on these facts, can you determine how many Freedonian senators are honest and how many are corrupt? If so, what is the answer?

Short Answer

Expert verified

The given conditions imply that there cannot be two honest senators. Therefore, since we know that there is at least one honest senator, there must be corrupt senators and 1 honest senator.

Step by step solution

01

Tips and Given

Translating sentences in natural language (such as English) into logical expressions is an essential part of specifying both hardware and software systems.

Given:

At least one of the Freedonian senators is honest and that, given any two Freedonian senators, at least one is corrupt.

02

Solve the given condition

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Most popular questions from this chapter

Let P(x),Q(x),R(x),andS(x) be the statements “xis a duck,” “xis one of my poultry,” “xis an officer,” and “xis willing to waltz,” respectively. Express each of these statements using quantifiers; logical connectives; andP(x),Q(x),R(x),andS(x).

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