The following categorical syllogisms all have more than three terms. Reduce the terms to three in each case by substituting synonyms or removing term complements (or both). Once the syllogism is in standard form, determine whether the argument is valid. If it is not, say which rule(s) it violates.

1.

1) All M are non-P.

2) No S are non-M.

So, 3) No S are P.

2.

1) All non-M are non-P.

2) All M are non-S.

So, 3) No S are P.

3.

1) No M are non-P.

2) All non-M are non-S.

So, 3) All S are P.

4.

1) Some P are M.

2) No M are non-S.

So, 3) Some S are P.

5.

1)All M are non-P.

2)Some M are not non-S.

So,3) Some S are not P.