Logical Deduction Logical Deduction - Section 4

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.

II is the converse of the second premise and so it holds.

No man is sky. No sky is road.

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

No man is sky. Some men are roads.

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 roads are not skies'.

No sky is road. Some men are roads.

As discussed above, it follows that 'Some men are not skies'.

Hence, only II follows.

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

All myths are fictions. No fiction is novel.

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 myth is novel'. Thus, I follows.

No fiction is novel. All novels are stories.

Since the middle term 'novels' is distributed twice in the premises, the conclusion must be particular. Since one premise is negative, the conclusion must be negative.

So, it follows that 'Some stories are not fictions'.

Hence, only I and III follow.

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.

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

No paper is pen. No pen is pencil.

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

All erasers are papers. No paper is pen.

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 eraser is pen'. III is the converse of this conclusion and so it holds.

Hence, only I and III follow.

IV is the converse of the second premise and so it holds.

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.

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.

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.

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.