# Validity of the arguments by using Euler Circles

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.

__________

Some C is not B.

B)

All B is A.

All C is A

__________

All C is B

#### Solution Preview

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(p=>~q)Λ(pΛr) => (rΛ~q)

The above given statement is proved true with the help of using truth tables. So, as the final column for all the inputs contain all True value, the above statement holds.

2)

The diagram shows the argument is ...