Statements: Some tigers are lions. Some lions are rabbits. Some rabbits are horses.

Conclusions:

1. Some tigers are horses.
2. Some rabbits are tigers.
3. Some horses are lions.
4. All horses are rabbits.

All oceans are rivers. Some springs are rivers.

Since the middle term 'rivers' is not distributed even once in the premises, no definite conclusion follows.

All wells are springs. Some springs are rivers.

Since the middle term 'springs' is not distributed even once in the premises, no definite conclusion follows. However, II and IV involve the extreme terms and form a complementary pair. Thus, either II or IV follows.

All doors are buses. All buses are leaves.

Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All doors are leaves'. III is the converse of this conclusion and so it holds.

All buses are leaves. No leaf is a flower.

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 bus is flower'. II is the converse of this conclusion and so it holds.

All doors are buses. No bus is flower.

As discussed above, it follows that 'No door is flower'. I is the converse of this conclusion and so it also holds.

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 trains are not jungles'.

No road is jungle. All flowers are jungles.

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 flower is road'. IV is the converse of this conclusion and so it holds.

Some trains are roads, No flower is road.

As discussed above, it follows that 'Some trains are not flowers'.

Since the middle term 'glasses' is not distributed even once in the premises, no definite conclusion follows.

Some glasses are bowls. No bowl is a plate.

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 glasses are not plates'.

Some bricks are trees. All trees are pens.

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

All trees are pens. All pens are boats.

Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All trees are boats'.

Some bricks are trees. All trees are boats.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bricks are boats'. Thus, IV follows. I is the converse of this conclusion and so it also holds.

Some spoons are bowls. All bowls are knives.

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

All bowls are knives. All knives are forks.

Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that.

'All bowls are forks'. Thus, II follows.

Some spoons are knives. All knives are forks.

Since one premise is particular, the conclusion must be particular and should not contain the middle term.

So, it follows that 'Some spoons are forks'. IV is the converse of this conclusion and so it follows.

Hence, II, III and IV follow.

Since both the premises are universal and affirmative, the conclusion must be universal affirmative (A-type) and should not contain the middle term. So, it follows that 'All pencils are skies'.

All birds are skies. All skies are hills.

As discussed above, it follows that 'All birds are hills'. Thus, IV follows.

All pencils are skies. All skies are hills.

Clearly, it follows that 'All pencils are hills'. Thus, I follows.

Hence, I and IV follow.

Since the middle term 'fruits' is distributed twice, the conclusion must be particular.

Since one premise is negative, the conclusion must be negative. So, it follows that

'Some stones are not trees'.

All fruits are stones. All stones are rains.

Clearly, it follows that 'All fruits are rains'. III is the converse of this conclusion and so it holds.

No tree is fruit, All fruits are rains.

As discussed above, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some rains are not trees'. However, II and IV involve only the extreme terms and form a complementary pair. Thus, either II or IV follows.

Since the middle term 'spectators' is not distributed even once in the premises, no definite conclusion follows.

Some spectators are theatres. Some theatres are dramas.

Since both the premises are particular, no definite conclusion follows.

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 door is fruit.'

Some flowers are doors. All doors are roads.

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

Some flowers are roads. No road is fruit.

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 flowers are not fruits'. II and IV involve the extreme terms and form a complementary pair. Thus, either II or IV follows.