Statements: Some towels are brushes. No brush is soap. All soaps are rats. Conclusions:  Some rats are brushes. No rat is brush. Some towels are soaps.

Some towels are brushes. No brush is soap.

Since one premise is particular and the other negative, the conclusion must be particular negative (O-type) and should not contain the middle term. So, it follows that 'Some towels are not soaps'. No brush is soap. All soaps are rats.

Since the middle term is distributed twice, the conclusion must be particular. Since one premise is negative, the conclusion must be negative. So, it follows that 'Some brushes are not rats'. Since I and II involve the same terms and form a complementary pair, so either I or II follows.