Validity Using Euler Circles and Truth Tables

In summary, the conversation is about using truth tables and Euler circles to determine the validity of arguments. The participants are struggling with the problem involving Euler circles and are seeking help on how to approach it.
  • #1
kma27
2
0
I'm so confused on how to tackle this problem:



1. Truth tables are related to Euler circles. Arguments in the form of Euler circles can be translated into statements using the basic connectives and the negation as follows:



Let p be “The object belongs to set A. “Let q be “the object belongs to set B.”


All A is B is equivalent to p -> q.

No A is B is equivalent to p ->~ q.

Some A is B is equivalent to p ^ q.

Some A is not B is equivalent to p ^ ~q.


Determine the validity of the next arguments by using Euler circles, then translate the statements into logical statements using the basic connectives, and using truth tables, determine the validity of the arguments. Compare your answers.


(a). No A is B.
Some C is A.
___________
Therefore Some C is not B.


(b) All B is A.
All C is A.
__________
Therefore All C is B.
 
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  • #2
?? What do you want help with? What have you done on (a) and (b)?
 
  • #3
I am having the same problem with that same problem.
 
  • #4
this question has me stumped also. I do not know the first step to getting started. any help will be greatly appreciated. thanks
 
Last edited:

Related to Validity Using Euler Circles and Truth Tables

1. What are Euler circles and truth tables?

Euler circles are visual representations of logical relationships between sets, and truth tables are tables that show the logical outcomes of different combinations of statements or propositions.

2. How are Euler circles and truth tables used to determine validity?

Euler circles and truth tables are used together to determine validity by visually representing the relationships between sets and logically evaluating the truth values of different statements or propositions. If the logical outcomes match in both the Euler circle and truth table, the argument is considered valid.

3. What is the difference between a valid and invalid argument?

A valid argument is one where the conclusion follows logically from the premises, while an invalid argument does not have a logical connection between the premises and the conclusion. In other words, a valid argument has a logically sound structure, while an invalid argument does not.

4. Do Euler circles and truth tables always determine validity?

No, Euler circles and truth tables are tools that can aid in determining validity, but they may not always provide a definitive answer. Other factors, such as ambiguity or missing information, can affect the validity of an argument.

5. Can Euler circles and truth tables be used for any type of argument?

Yes, Euler circles and truth tables can be used for any type of argument, as long as the premises and conclusion can be represented visually and logically evaluated. However, they may not always be the most efficient or effective method for determining validity, and other techniques may be more appropriate for certain types of arguments.

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