Exercise: Logical Deduction

Questions for: Logical Deduction

Statements: Many scooters are trucks. All trucks are trains.

Conclusions:

  1. Some scooters are trains.
  2. No truck is a scooter.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: A
Since the first premise is particular, the conclusion must be particular and should not contain the middle term. Thus, only I follows.
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Statements: All poles are guns. Some boats are not poles.

Conclusions:

  1. All guns are boats.
  2. Some boats are not guns.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: D
Clearly, the term 'guns' is distributed in both the conclusions without being distributed in any of the premises. So, neither conclusion follows.
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Statements: All jungles are tigers. Some tigers are horses.

Conclusions:

  1. Some horses are jungles.
  2. No horse is jungle.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: C
Since the middle term 'tigers' is not distributed even once in the premises, no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. So, either I or II follows.
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Statements: Some dreams are nights. Some nights are days.

Conclusions:

  1. All days are either nights or dreams.
  2. Some days are nights.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: B
Since both the premises are particular, no definite conclusion follows. However, II is the converse of the second premise and thus it holds.
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Statements: All hill stations have a sun-set point. X is a hill station.

Conclusions:

  1. X has a sun-set point.
  2. Places other than hill stations do not have sun-set points.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: A
Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, only I follows.
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