Translating sentence into symbols

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SUMMARY

The discussion focuses on translating the English sentence "The numbers four and five aren't both prime, but the numbers five and seven are" into logical symbols. The correct representation is achieved by recognizing that "but" functions as "and" in logical terms. The final translation is expressed as ~(F&I) & (I&S), where F represents four, I represents five, and S represents seven. This clarification emphasizes the importance of understanding logical connectors in symbolic logic.

PREREQUISITES
  • Understanding of basic symbolic logic
  • Familiarity with logical operators such as AND (&), OR (v), and NOT (~)
  • Knowledge of prime numbers and their properties
  • Ability to translate English sentences into logical expressions
NEXT STEPS
  • Study the use of logical operators in propositional logic
  • Learn about the nuances of translating natural language into formal logic
  • Explore examples of logical statements involving negation and conjunction
  • Practice with more complex sentences to enhance translation skills
USEFUL FOR

Students of philosophy, mathematics, or computer science, as well as anyone interested in improving their skills in symbolic logic and logical reasoning.

Nathew
I'm having trouble with translating this english sentence into logic symbols.

The sentence is

The numbers four and five aren't both prime, but the numbers five and seven are.

I was thinking ~(F&I)v(IvS) but I really don't know how to deal with the "but".

Thanks
 
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so
~(F&I)&(I&S)
?
 
I meant the upside down v commonly used in logic for AND. The v itself is used for OR.
 
Nathew said:
I was thinking ~(F&I)v(IvS) but I really don't know how to deal with the "but".
Jedishrfu is exactly right. In logic, "but" is equivalent to "and." If you say, for example "x is A but y is B," what you're really saying is "x is A and y is B," and the "but" merely points out that there is some sort of contrast that you want draw the listener's attention to.
 

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