Exercise: Logical Deduction

Questions for: Logical Deduction

Statements: All jungles are buses. All books are buses. All fruits are books.

Conclusions:

  1. Some fruits are jungles.
  2. Some buses are books.
  3. Some buses are jungles.
  4. All fruits are buses.

A:
Only I, II and III follow
B:
Only I, II and IV follow
C:
Only II, III and IV follow
D:
All follow
Answer: C

III is the converse of the first premise and II is the converse of the second premise.

So, both of them hold.

All fruits are books. All books are buses.

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 fruits are buses'. Thus, IV follows.

All jungles are buses. All books are buses.

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

All fruits are buses. All books are buses.

As discussed above, no definite conclusion can be drawn.

All jungles are buses. All fruits are buses.

Again, no definite conclusion follows.

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Statements: No table is fruit. No fruit is window. All windows are chairs.

Conclusions:

  1. No window is table.
  2. No chair is fruit.
  3. No chair is table.
  4. All chairs are windows.

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

No table is fruit. No fruit is window.

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

No fruit is window. All windows are chairs.

Since the middle term 'windows' is distributed twice and one premise is negative, the conclusion must be particular negative. So, it follows that 'Some chairs are not fruits'.

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Statements: Some tapes are discs. Some discs are cassettes. Some cassettes are songs.

Conclusions:

  1. Some songs are discs.
  2. Some cassettes are tapes.
  3. Some songs are tapes.
  4. No song is a disc.

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

Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn. However, I and IV involve the extreme terms of the second and third premises and form a complementary pair. Thus, either I or IV follows.

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Statements: Some papers are cats. All cats are bats. No bat is horse.

Conclusions:

  1. Some papers are horses.
  2. No horse is cat.
  3. Some bats are papers.
  4. All papers are bats.

A:
Only I and II follow
B:
Only II and III follow
C:
Only III and IV follow
D:
Only I and IV follow
Answer: B

Some papers are cats. All cats are bats.

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

All cats are bats. No bat is horse.

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 cat is horse'. II is the converse of this conclusion and so it holds.

Some papers are bats. No bat is horse.

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 papers are not horses'.

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Statements: All buildings are windows. No toys is building. Some tigers are toys.

Conclusions:

  1. Some tigers are buildings.
  2. Some windows are tigers.
  3. All toys are tigers.
  4. Some windows are toys.

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

No toy is building. All buildings are windows.

Since the middle term 'buildings' is distributed twice and one premise is negative, the conclusion must be particular negative and should not contain the middle term.

So, it follows that 'Some windows are not toys'.

Some tigers are toys. No toy is building.

Since one premise is particular and the other premise is negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some tigers are not buildings'.

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