Exercise: Logical Deduction

Questions for: Logical Deduction

Statements: No house is school. All colleges are schools. All schools are teachers.

Conclusions:

  1. No house is teacher.
  2. All colleges are teachers.
  3. Some teachers are not houses.
  4. No college is house.

A:
None follows
B:
Only either I or IV follows
C:
Only II, III and IV follow
D:
All follow
Answer: C

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'.

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Statements: All needles are threads. All threads are boxes. All trees are boxes.

Conclusions:

  1. No needle is tree.
  2. Some trees are threads.
  3. Some boxes are needles.
  4. Some trees are needles.

A:
None follows
B:
Only either I or IV follows
C:
Only either I or IV, and II follow
D:
Only III follows
Answer: E

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.

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Statements: All doors are roads. No road is fruit. Some flowers are doors.

Conclusions:

  1. Some fruits are doors.
  2. Some fruits are flowers.
  3. Some roads are flowers.
  4. No fruit is flower.

A:
Only either II or III, and IV follow
B:
Only either II or IV, and III follow
C:
Only either II or IV, and I follow
D:
Only either II or IV follows
Answer: B

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.

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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.

A:
None follows
B:
Only I and III follow
C:
Only II follows
D:
Only II and IV follow
Answer: A

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.

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Statements: No tree is fruit. All fruits are stones. All stones are rains.

Conclusions:

  1. No stone is tree.
  2. No rain is tree.
  3. Some rains are fruits.
  4. Some rains are trees.

A:
Only either II or III, and I follow
B:
None follows
C:
Only either II or IV, and III follow
D:
All follow
Answer: C

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.

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