Since the middle term 'tigers' is not distributed even once in the premises, no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. So, either I or II follows.
statements: Some hills are rivers. Some rivers are deserts. All deserts are roads. Conclusions: I.Some roads are rivers. II.Some roads are hills. III.Some deserts are hills.
Some hills are rivers. Some rivers are deserts.
Since both the premises are particular, no definite conclusion follows.
Some rivers are deserts. All deserts are roads.
Since one premise is particular, the conclusion must be particular and shouldn't contain the middle term. So, it follows that 'Some rivers are roads'. I is the converse of this conclusion and so it holds.
Some hills are rivers. Some rivers are roads.
Again, since both the premises are particular, no definite conclusion follows.
statements: Some saints are balls. All balls are bats. Some tigers are balls. Conclusions: I.Some bats are tigers. II.Some saints are bats. III.All bats are balls.
Some saints are balls. All balls are bats.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some saints are bats'. Thus, II follows. Some tigers are balls. All balls are bats.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some tigers are bats'. I is the converse of this conclusion and so it holds.
statements: All tigers are jungles. No jungle is bird. Some birds are rains. Conclusions: I.No rain is jungle. II.Some rains are jungles. III.No bird is tiger.
All tigers are jungles. No jungle is bird.
Since both the premises are universal and one premise is negative, the conclusion must be universal negative (E-type) and should not contain the middle term.
So, it follows that 'No tiger is bird'. III is the converse of this conclusion and so it holds.
No jungle is bird. Some birds are rains.
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 jungles are not rains'.
Since I and II also involve the same terms and form a complementary pair, so either I or II follows.
statements: No rabbit is lion. Some horses are lions. All rabbits are tables. Conclusions: I.Some tables are lions. II.Some horses are rabbits. III.No lion is table.
Some horses are lions. No rabbit is lion.
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 horses are not rabbits'.
All rabbits are tables. No rabbit is lion.
Since the middle term 'rabbits' is distributed twice, the conclusion must be particular.
Since one premise is negative, the conclusion must be negative. So, it follows that 'Some tables are not lions'. Since I and III involve the same terms and form a complementary pair, so either I or III follows.
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