Logical Reasoning - Logical Deduction
In each of the following questions, three statements are given followed by four conclusions numbered I, II, III and TV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: All doors are buses. All buses are leaves. No leaf is a flower.
Conclusions:
- No flower is a door.
- No flower is a bus.
- Some leaves are doors.
- Some leaves are buses.
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.
Statements: All oceans are rivers. Some springs are rivers. All wells are springs.
Conclusions:
- Some springs are oceans.
- Some wells are rivers.
- Some rivers are oceans.
- No well is river.
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.
Statements: Some tigers are lions. Some lions are rabbits. Some rabbits are horses.
Conclusions:
- Some tigers are horses.
- Some rabbits are tigers.
- Some horses are lions.
- All horses are rabbits.
Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn.
Statements: Some spoons are bowls. All bowls are knives. All knives are forks.
Conclusions:
- All spoons are forks.
- All bowls are forks.
- Some knives are bowls.
- Some forks are spoons.
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.
Statements: All pencils are birds. All birds are skies. All skies are hills.
Conclusions:
- All pencils are hills.
- All hills are birds
- All skies are pencils.
- All birds are hills.
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.