Exercise: Logical Deduction

Questions for: Logical Deduction

Statements: Some pastries are toffees. All toffees are chocolates.

Conclusions:

  1. Some chocolates are toffees.
  2. Some toffees are not pastries.
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. Thus, it follows that 'Some pastries are chocolates', I is the converse of the second premise and so it holds. Since both the premises are affirmative, the conclusion cannot be negative. Thus, II does not follow.
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Statements: All young scientists are open-minded. No open-minded men are superstitious.

Conclusions:

  1. No scientist is superstitious.
  2. No young people are superstitious.
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 subject in both the conclusions is vague. The true conclusion is 'No young scientist is superstitious'. Thus, neither I nor II follows,
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Statements: All men are dogs. All dogs are cats.

Conclusions:

  1. All men are cats.
  2. All cats are men.
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. However, conclusion II, being an A-type proposition, distributes the term 'cats'.

Since the term 'cats' is distributed in II without being distributed in any of the premises, so conclusion II cannot follow. Thus, only I follows.
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Statements: All water is divine. All temples are divine.

Conclusions:

  1. All water is temple.
  2. All temples are water.
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 'divine' is not distributed even once in the premises, no definite conclusion can be drawn.
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Statements: Some hens are cows. All cows are horses.

Conclusions:

  1. Some horses are hens.
  2. Some hens are horses.
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 one premise is particular, the conclusion must be particular and should not contain the middle term. So, II follows. I is the converse of II and so it also holds.
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