Exercise: Logical Deduction

Questions for: Logical Deduction

Statements: All branches are flowers. All flowers are leaves.

Conclusions:

  1. All branches are leaves.
  2. All leaves are branches.
  3. All flowers are branches.
  4. Some leaves are branches.

A:
None follows
B:
Only I and IV follow
C:
Only II and III follow
D:
All follow
Answer: B
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 branches are leaves'. Thus, I follows. IV is the converse of this conclusion and so it also holds.
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Statements: All cars are cats. All fans are cats.

Conclusions:

  1. All cars are fans
  2. Some fans are cars.
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 'cats' is not distributed even once in the premises, no definite conclusion follows.
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Statements: All artists are smokers. Some smokers are drunkards.

Conclusions:

  1. All smokers are artists.
  2. Some drunkards are not smokers.
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 'smokers' is not distributed even once in the premises, no definite conclusion follows.
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Statements: All pens are roads. All roads are houses.

Conclusions:

  1. All houses are pens.
  2. Some houses are pens.
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 universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, it follows that 'All pens are houses'. II is the converse of this conclusion and so it holds. Since the term 'houses' is distributed in I without being distributed in any of the premises, so I does not follow.
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Statements: All boys are honest. Sachin is honest.

Conclusions:

  1. Sachin is a boy.
  2. All honest persons are boys.
A:
Only conclusion I follows
B:
Only conclusion II follows
C:
Either I or II follows
D:
Neither I nor II follows
Answer: D
Both the premises are A type propositions. So, the middle term 'honest' forming the predicate in each is not distributed in either. Since the middle term is not distributed even once, no definite conclusion follows.
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