Logical Deduction - 05

01. Statements :No gentleman is poor. All gentlemen are rich.

Conclusions :
I. No poor man is rich.
II. No rich man is poor.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Neither I nor II follows
Answer:- 1
Explanation:-

Solution:
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.

02. Statements :Some dedicated souls are angels. All social workers are angels.

Conclusions :
I. Some dedicated souls are social workers.
II. Some social workers are dedicated souls.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Neither I nor II follows
Answer:- 1
Explanation:-

Solution:
The first premise is an I type proposition. So, the middle term 'angels' forming the predicate is not distributed. The second premise is an A type proposition. So, the middle term 'angels' forming the predicate is not distributed. Since the middle term is not distributed even once in the premises, no definite conclusion follows.

03. Statements :All fish are tortoise. No tortoise is a crocodile.

Conclusions :
I. No crocodile is a fish.
II. No fish is a crocodile.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Both I and II follow
Answer:- 1
Explanation:-

Solution:
Since both the premises are universal and one premise is negative, the conclusion must be universal negative. Also, the conclusion should not contain the middle term. So, II follows; I is the converse of II and thus it also holds.

04. Statements :All roads are poles. No pole is a house.

Conclusions :
I. Some roads are houses.
II. Some houses are poles.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Neither I nor II follows
Answer:- 1
Explanation:-

Solution:
Since both the premises are universal and one premise is negative, the conclusion must be universal negative. So, neither I nor II follows.

05. Statements :All flowers are trees. No fruit is tree.

Conclusions :
I. No fruit is flower.
II. Some trees are flowers.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Both I and II follow
Answer:- 1
Explanation:-

Solution:
As discussed above, the conclusion must be universal negative and should not contain the middle term. So, it follows that 'No flower is fruit'. I is the converse of this conclusion and thus it follows. II is the converse of the first premise and so it also holds.

06. Statements :No bat is ball. No ball is wicket.

Conclusions :
I. No bat is wicket.
II. All wickets are bats.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Neither I nor II follows
Answer:- 1
Explanation:-

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

07. Statements :All roads are waters. Some waters are boats.

Conclusions :
I. Some boats are roads.
II. All waters are boats.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Neither I nor II follows
Answer:- 1
Explanation:-

Solution:
The first premise is A type and distributes the subject. So, the middle term 'waters' which forms its predicate, is not distributed. The second premise is I type and does not distribute either subject or predicate. So, the middle term 'waters' forming its subject is not distributed. Since the middle term is not distributed even once in the premises, no definite conclusion follows.

08. Statements :Some doctors are fools. Some fools are rich.

Conclusions :
I. Some doctors are rich
II. Some rich are doctors.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Neither I nor II follows
Answer:- 1
Explanation:-

Solution:
Since both the premises are particular, no definite conclusion follows.

09. Statements :All mangoes are golden in colour. No golden-coloured things are cheap.

Conclusions :
I. All mangoes are cheap.
II. Golden-coloured mangoes are not cheap.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Neither I nor II follows
Answer:- 1
Explanation:-

Solution:
Clearly, the conclusion must be universal negative and should not contain the middle term. So, it follows that 'No mango is cheap'. Since all mangoes are golden in colour, we may substitute 'mangoes' with 'golden-coloured mangoes'. Thus, II follows.

10. Statements :All bags are cakes. All lamps are cakes.

Conclusions :
I. Some lamps are bags.
II. No lamp is bag.

  • 1Only conclusion I follows
  • 2Only conclusion II follows
  • 3Either I or II follows
  • 4Neither I nor II follows
Answer:- 1
Explanation:-

Solution:
Since the middle term 'cakes' 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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