Logical Deduction - 03

01. Statements : Some bottles are drinks. All drinks are cups.

Conclusions :
I. Some bottles are cups.
II. Some cups are drinks.
III. All drinks are bottles.
IV. All cups are drinks.

  • 1Only I and II follow
  • 2Only II and III follow
  • 3Only II and IV follow
  • 4Only III and IV follow
Answer:- 1
Explanation:-

Solution:
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bottles are cups'. Thus, I follows. II is the converse of the second premise and so it also holds.

02. Statements : Some books are pens. No pen is pencil.

Conclusions :
I. Some pens are books.
II. Some pencils are books.
III. Some books are not pencils.
IV. All pencils are books.

  • 1Only I follows
  • 2Only II and III follow
  • 3Only I and III follow
  • 4Only I and II follow
Answer:- 1
Explanation:-

Solution:
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. Thus, III follows. I is the converse of the first premise and so it also holds.

03. Statements : All terrorists are guilty. All terrorists are criminals.

Conclusions :
I. Either all criminals are guilty or all guilty are criminals.
II. Some guilty persons are criminals.
III. Generally criminals are guilty.
IV. Crime and guilt go together.

  • 1Only I follows
  • 2Only I and III follow
  • 3Only II follows
  • 4Only II and IV follow
Answer:- 1
Explanation:-

Solution:
Since the middle term 'terrorists' is distributed twice in the premises, the conclusion cannot be universal. So, it follows that 'Some guilty persons are criminals'. Thus, II holds.

04. Statements : Some tables are TVs. Some TVs are radios.

Conclusions :
I. Some tables are radios.
II. Some radios are tables.
III. All radios are TVs.
IV. All TVs are tables.

  • 1None follows
  • 2All follow
  • 3Only I and III follow
  • 4Only II and IV follow
Answer:- 1
Explanation:-

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

05. Statements : All politicians are honest. All honest are fair.

Conclusions :
I. Some honest are politicians.
II. No honest is politician.
III. Some fair are politicians.
IV. All fair are politicians.

  • 1None follows.
  • 2Only I follows.
  • 3Only I and II follow.
  • 4Only I and III follow
Answer:- 1
Explanation:-

Solution:
Clearly, it follows that 'All politicians are fair'. I is the converse of the first premise, while III is the converse of the above conclusion. So, both I and III hold.

06. Statements : All aeroplanes are trains. Some trains are chairs.

Conclusions :
I. Some aeroplanes are chairs.
II. Some chairs are aeroplanes.
III. Some chairs are trains.
IV. Some trains are aeroplanes.

  • 1None follows
  • 2Only I and II follow
  • 3Only II and III follow
  • 4Only III and IV follow
Answer:- 1
Explanation:-

Solution:
Since the middle term 'trains' is not distributed even once in the/premises, no definite conclusion follows. However, III is the converse of the second premise while IV is the converse of the first premise. So, both of them hold.

07. Statements : Some bags are pockets. No pocket is a pouch.

Conclusions :
I. No bag is a pouch.
II. Some bags are not pouches.
III. Some pockets are bags.
IV. No pocket is a bag,

  • 1None follows
  • 2Only I and III follow
  • 3Only II and III follow
  • 4Only either I or IV follows
Answer:- 1
Explanation:-

Solution:
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, II follows. III is the converse of the first premise and thus it also holds.

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

Conclusions :
I. All branches are leaves.
II. All leaves are branches.
III. All flowers are branches.
IV. Some leaves are branches.

  • 1None follows
  • 2Only I and IV follow
  • 3Only II and III follow
  • 4All follow
Answer:- 1
Explanation:-

Solution:
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.

09. Statements :All cars are cats. All fans are cats.

Conclusions :
I. All cars are fans.
II. Some fans are cars.

  • 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 'cats' is not distributed even once in the premises, no definite conclusion follows.

10. Statements :All cars are cats. All fans are cats.

Conclusions :
I. All cars are fans
II. Some fans are cars.

  • 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 'cats' is not distributed even once in the premises, no definite conclusion follows.

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