Finding a logical formula (wff) for an englsh expression

In summary, a wff (well-formed formula) is a mathematical formula used to represent logical statements in a precise and logical manner. It is commonly used in scientific research to analyze complex ideas and arguments. The process for finding a wff for an English expression involves breaking it down into logical components and using symbols and operators to create the formula. While wffs are useful, they have limitations in capturing natural language and emotions and require a strong understanding of logic. However, they can be translated back into English by applying the inverse process.
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Homework Statement



Suppose P(x) is a statement with a free variable x. Find a formula, using logical symbols, that means "there are exactly two values of x for which P(x) is true."


Homework Equations





The Attempt at a Solution




(∃x)(∃y)(∀z)(P(x) ∧ P(y) ∧ P(z) → ( x=z ∨ y=z) ∧ x≠y)

Is this valid?
 
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1. What is a wff?

A wff stands for "well-formed formula" and is a mathematical formula that follows a set of rules and symbols to represent logical statements.

2. How is a wff used in scientific research?

Wffs are used in scientific research to represent complex ideas and arguments in a precise and logical manner. They allow for the manipulation and analysis of logical statements to draw conclusions and make predictions.

3. What is the process for finding a wff for an English expression?

The process involves breaking down the English expression into its logical components, assigning symbols to each component, and then using logical operators to create a wff that accurately represents the original expression.

4. Are there any limitations to using wffs?

While wffs are a useful tool for representing logical statements, they have limitations in their ability to capture the nuances of natural language and emotions. They also require a solid understanding of logic and syntax to create and interpret.

5. Can a wff be translated back into English?

Yes, a wff can be translated back into English by applying the inverse process of creating a wff. This involves breaking down the wff into its logical components and then using the corresponding symbols and logical operators to reconstruct the original English expression.

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