Exercise: Logical Deduction

Questions for: Logical Deduction

Statements: All film stars are playback singers. All film directors are film stars.

Conclusions:

  1. All film directors are playback singers.
  2. Some film stars are film directors.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: E
Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, I follows. II is the converse of the second premise and so it also holds.
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Statements: All good athletes win. All good athletes eat well.

Conclusions:

  1. All those who eat well are good athletes.
  2. All those who win eat well.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: D
Since the middle term 'good athletes' is distributed twice in the premises, the conclusion must be particular and should not contain the middle term. So it follows that 'Some of those who win, eat well'.
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Statements: All fishes are grey in colour. Some fishes are heavy.

Conclusions:

  1. All heavy fishes are grey in colour.
  2. All light fishes are not grey in colour.
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 one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some heavy things are grey in colour'. I is a cumulative result of this conclusion and the first premise. Thus, only I holds.
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Statements: Some swords are sharp. All swords are rusty

Conclusions:

  1. Some rusty things are sharp.
  2. Some rusty things are not sharp.
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 one premise is particular, the conclusion must be particular and should not contain the middle term. So, I follows. Since both the premises are affirmative, the conclusion cannot be negative. Thus, II does not follow.
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Statements: No gentleman is poor. All gentlemen are rich.

Conclusions:

  1. No poor man is rich.
  2. No rich man is poor.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: D
The first premise is an E-type proposition, So, the middle term 'gentleman' forming the subject is distributed. The second premise is an A-type proposition. So, the middle term 'gentlemen' forming the subject is distributed. Since the middle term is distributed twice, the conclusion cannot be universal. Since one premise is negative, the conclusion must be negative. Thus, it follows that 'Some rich men are not poor'. Thus, neither I nor II follows.
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