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: No tree is fruit. All fruits are stones. All stones are rains.
Conclusions:
- No stone is tree.
- No rain is tree.
- Some rains are fruits.
- Some rains are trees.
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.
Statements: All players are spectators. Some spectators are theatres. Some theatres are dramas.
Conclusions:
- Some dramas are spectators.
- Some players are dramas.
- Some theatres are players.
- All spectators are players.
All players are spectators. Some spectators are theatres.
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.
Statements: All doors are roads. No road is fruit. Some flowers are doors.
Conclusions:
- Some fruits are doors.
- Some fruits are flowers.
- Some roads are flowers.
- No fruit is flower.
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.
Statements: All needles are threads. All threads are boxes. All trees are boxes.
Conclusions:
- No needle is tree.
- Some trees are threads.
- Some boxes are needles.
- Some trees are needles.
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.
Statements: No house is school. All colleges are schools. All schools are teachers.
Conclusions:
- No house is teacher.
- All colleges are teachers.
- Some teachers are not houses.
- No college is house.
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'.