Statements: Some papers are cats. All cats are bats. No bat is horse. Conclusions: Some papers are horses. No horse is cat. Some bats are papers. All papers are bats.

Some papers are cats. All cats are bats.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some papers are bats'. III is the converse of this conclusion and so it holds.

All cats are bats. No bat is horse.

Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, it follows that 'No cat is horse'. II is the converse of this conclusion and so it holds.

Some papers are bats. No bat is horse.

Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some papers are not horses'.