Statements: All players are spectators. Some spectators are theatres. Some theatres are dramas.

Conclusions:

1. Some dramas are spectators.
2. Some players are dramas.
3. Some theatres are players.
4. All spectators are players.

No tree is fruit. All fruits are stones.

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.

All pencils are birds. All birds are skies.

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.

III is the converse of the second premise and so it 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 each combination of premises shall contain two particular premises, no definite conclusion can be drawn.

III is the converse of the first premise and so it holds.

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 roads. No road is fruit.

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.

All needles are threads. All threads are boxes.

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 needles are boxes'. III is the converse of this conclusion and so it holds.

All threads are boxes. All trees are boxes.

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

All needles are boxes. All trees are boxes.

Again, since the middle term 'boxes' is not distributed even once in the premises, no definite conclusion can be drawn. However, I and IV involve the extreme terms of these two statements and form a complementary pair. Thus, either I or IV follows.

All colleges are schools. No house is school.

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 college is house'. Thus, IV follows.

All colleges are schools. All schools are teachers.

Clearly, it follows that 'All colleges are teachers'. Thus, II follows.

No house is school. All schools are teachers.

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

Since one premise is negative, the conclusion must be negative. So, it follows that 'Some teachers are not houses'.

III is the converse of the third premise and so it holds.

Some pearls are stones. Some stones are diamonds.

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

Some stones are diamonds. No diamond is a gem.

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 stones are not gems'.

However, I and IV involve the extreme terms of the three premises and form a complementary pair, Thus, either I or IV follows.

All rods are bricks. Some bricks are ropes.

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

Some bricks are ropes. All ropes are doors.

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

All rods are bricks. Some bricks are doors.

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

However, I and III involve the extreme terms. But, since they are not contradictory, they do not form a complementary pair.

Hence, only II follows.