Explanation Definition: For a letter game with three undefined terms, the letters M , I and U and one definition which defines x as any string of I ’s and U ’s, the four axioms defined are: 1. Addition rule – For a string of letters ending in I , letter U may be added at the end. 2. Doubling rule – If there is Mx , then x may be added to get Mxx . 3. Substitution rule – If there are three I ’s ( III ), then this string can be replaced by U . 4 . Deletion rule – If UU occurs, it is dropped. Proof: Consider the given string of letters MIII . It has to be proved that it is equivalent to M . Use addition rule and add a U at the end of MIII. M I I I → M I I I U Use substitution rule and replace three I ’s with U

Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

13th Edition

ISBN: 9781337605076

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 3.5, Problem 9PS

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To prove:

The theorem if given MIII, then it can be equivalent to M in the letter game with three undefined terms of letters M,I and U and one definition “x meaning string of I’s and U’s”.

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Chapter 3.5, Problem 8PS

Chapter 3.5, Problem 10PS

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Bundle: Nature Of Mathematics, Loose-leaf Version, 13th + Webassign Printed Access Card For Smith's Nature Of Mathematics, 13th Edition, Single-term

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To prove: The theorem if given MIII , then it can be equivalent to M in the letter game with three undefined terms of letters M , I and U and one definition “ x meaning string of I ’s and U ’s”.

Solution Summary: The author explains the sequence of steps to prove the theorem that given MIII is equivalent to M in the letter game with three undefined terms.

Videos

To prove:

The theorem if given MIII, then it can be equivalent to M in the letter game with three undefined terms of letters M,I and U and one definition “x meaning string of I’s and U’s”.

Want to see the full answer?

Chapter 3 Solutions

To prove: The theorem if given MIII , then it can be equivalent to M in the letter game with three undefined terms of letters M , I and U and one definition “ x meaning string of I ’s and U ’s”.

Solution Summary: The author explains the sequence of steps to prove the theorem that given MIII is equivalent to M in the letter game with three undefined terms.

Videos

To prove: The theorem if given MIII, then it can be equivalent to M in the letter game with three undefined terms of letters M,I and U and one definition “x meaning string of I’s and U’s”.

Want to see the full answer?

Chapter 3 Solutions

To prove:

The theorem if given MIII, then it can be equivalent to M in the letter game with three undefined terms of letters M,I and U and one definition “x meaning string of I’s and U’s”.