Proving Syllogisms

There are 11 buttons in the present system. Their use can be explained in the following manner:

Clear

Clears the screen.

Picks a new syllogism at random.

Displays a help message.

Will - if possible - prove new propositions using the following deduction:

All Y are Z

All X are Y

Therefore: All X are Z

Will - if possible - prove new propositions using the following deduction:

All Y are Z

Some X are Y

Therefore: Some X are Z

Will - if possible - prove new propositions using the following deduction:

All X are Y

Therefore: All non-Y are non-X

(Here, non-X corresponds to the set of elements not belonging to X.)

Will - if possible - prove new propositions using the following deduction:

Some X are Y

Therefore: Some Y are X

Will - if possible - prove new propositions using the following deduction:

All X are Y

Therefore:Some X are Y

When you have explored the provability of the syllogism in question, it should be evaluated.

Use the button...

Invalid, if you after your explorarion find that the syllogism in question is invalid.
Valid (Ex is needed), if you think that the syllogism in question is provable only if Ex is allowed.
Valid (Ex is not needed), if you think that the syllogism in question is provable without the use of Ex.