A set M of numbers is defined recursively by 1. 2 and 3 belong to M. 2. If x and y

Chapter 3, Problem 48

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QUESTION:

A set M of numbers is defined recursively by 1. 2 and 3 belong to M. 2. If x and y belong to M, so does x * y. Which of the following numbers belong to M? a. 6 b. 9 c. 16 d. 21 e. 26 f. 54 g. 72 h. 218

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QUESTION:

A set M of numbers is defined recursively by 1. 2 and 3 belong to M. 2. If x and y belong to M, so does x * y. Which of the following numbers belong to M? a. 6 b. 9 c. 16 d. 21 e. 26 f. 54 g. 72 h. 218

ANSWER:

Step 1 of 2

A set M of numbers is defined recursively by

1. 2 and 3 belong to M.

2. If x and y belong to M, so does x * y

Since , therefore,

Since , therefore, .

Since , therefore, . It follows that .

We know that

By given hypothesis, , but . Therefore, .

We know that

By given hypothesis, , but . Therefore, .

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