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 MI . It has to be proved that it is equivalent to MIIUIIU . Use doubling rule and add a I at the end of MI. M I → M I I Again use doubling rule and add a I at the end of MI. M I I → M I I I Again use doubling rule and add a I at the end of MIII. M I I I → M I I I I Once again use doubling rule and add a I at the end of MIIII

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Chapter 3.5, Problem 12PS

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The theorem if given MI, then it can be equivalent to MIIUIIU 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 11PS

Chapter 3.5, Problem 13PS

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To prove: The theorem if given MI , then it can be equivalent to MIIUIIU 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 MI, is equivalent to MIIUIIU in the letter game with three undefined terms.

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To prove:

The theorem if given MI, then it can be equivalent to MIIUIIU 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 MI , then it can be equivalent to MIIUIIU 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 MI, is equivalent to MIIUIIU in the letter game with three undefined terms.

Videos

To prove: The theorem if given MI, then it can be equivalent to MIIUIIU 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 MI, then it can be equivalent to MIIUIIU 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”.