Translating sentence into symbols

In summary, the conversation is about translating an English sentence into logic symbols. The sentence states that the numbers four and five are not both prime, but the numbers five and seven are. The person suggests using ~(F&I)&(I&S) to represent this, but is unsure about how to handle the "but" in the sentence. It is then clarified that "but" can be replaced with "and" in logic, making the correct representation ~(F&I)&(I&S).
  • #1
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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  • #3
so
~(F&I)&(I&S)
?
 
  • #4
I meant the upside down v commonly used in logic for AND. The v itself is used for OR.
 
  • #5
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.
 

FAQ: Translating sentence into symbols

1. What is the purpose of translating sentences into symbols?

Translating sentences into symbols is a method used in mathematical logic to represent statements and arguments in a more precise and concise way. It allows for complex ideas to be expressed in a standardized format, making it easier to analyze and evaluate logical relationships between statements.

2. How do you translate a sentence into symbols?

To translate a sentence into symbols, you first need to identify the key logical operators and connectives, such as "and," "or," "if...then," and "not." Then, assign variables to represent the components of the sentence and use the appropriate symbols to represent the logical relationships between them. The resulting symbolic representation should accurately convey the meaning of the original sentence.

3. What are the benefits of using symbols in logical reasoning?

Using symbols in logical reasoning allows for a more systematic and organized approach to analyzing and evaluating arguments. It also reduces the potential for confusion and misinterpretation, as symbols have clear and unambiguous meanings. Additionally, symbols can be manipulated and combined using logical rules, making it easier to derive conclusions from multiple statements.

4. Are there any limitations to translating sentences into symbols?

While translating sentences into symbols can be a useful tool in logical reasoning, it is not without limitations. It may not capture the full complexity and nuance of natural language, and it requires a certain level of familiarity with logical notation. Additionally, it may not always be applicable to real-world situations, as some concepts and ideas cannot be easily translated into symbols.

5. Can symbols be translated back into sentences?

Yes, symbols can be translated back into sentences by using the logical rules and definitions that were used in the translation process. However, the resulting sentences may not always have the same exact wording or structure as the original sentence, as the symbolic representation is often more concise and abstract. It is important to carefully consider the meaning and context of the symbols when translating them back into sentences.

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