Logical Reasoning - Logical Deduction

In each of the following questions, three statements are given followed by four conclusions numbered I, II, III and TV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

1. 

Statements: All benches are desks. Some desks are roads. All roads are pillars.

Conclusions:

  1. Some pillars are benches.
  2. Some pillars are desks.
  3. Some roads are benches.
  4. No pillar is bench.

A. None follows
B. Only either I or IV, and III follow
C. Only either I or IV follows
D. Only either I or IV, and II follow
E. All follow

Answer: Option D

Explanation:

All benches are desks. Some desks are roads.

Since the middle term 'desks' is not distributed even once in the premises, no definite conclusion follows.

Some desks are roads. All roads are pillars.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some desks are pillars'. II is the converse of this conclusion and so it holds.

All benches are desks. Some desks are pillars.

Since the middle term 'desks' is not distributed even once in the premises, no definite conclusion follows. However, I and IV involve the extreme terms and form a complementary pair. So, either I or IV follows.


2. 

Statements: Some dogs are rats. All rats are trees. Some trees are not dogs.

Conclusions:

  1. Some trees are dogs.
  2. All dogs are trees.
  3. All rats are dogs.
  4. No tree is dog.

A. None follows
B. Only I follows
C. Only I and II follow
D. Only II and III follow
E. All follow

Answer: Option B

Explanation:

Some dogs are rats. All rats are trees.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some dogs are trees'. I is the converse of this conclusion and so it holds.

All rats are trees. Some trees are not dogs.

Since the middle term 'trees' is not distributed even once in the premises, no definite conclusion follows.


3. 

Statements: Some bricks are trees. All trees are pens. All pens are boats.

Conclusions:

  1. Some boats are bricks.
  2. Some pens are bricks.
  3. Some trees are bricks.
  4. Some bricks are boats.

A. Only I and II follow
B. Only III and IV follow
C. None follows
D. All follow
E. None of these

Answer: Option D

Explanation:

III is the converse of the first premise and so it holds.

Some bricks are trees. All trees are pens.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bricks are pens'. II is the converse of this conclusion and so it holds.

All trees are pens. All pens are boats.

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 trees are boats'.

Some bricks are trees. All trees are boats.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bricks are boats'. Thus, IV follows. I is the converse of this conclusion and so it also holds.


4. 

Statements: All cups are glasses. Some glasses are bowls. No bowl is a plate.

Conclusions:

  1. No cup is a plate.
  2. No glass is a plate.
  3. Some plates are bowls.
  4. Some cups are not glasses.

A. None follows
B. Only either I or III follows
C. Only II and III follow
D. Only III and IV follow
E. None of these

Answer: Option A

Explanation:

All cups are glasses. Some glasses are bowls.

Since the middle term 'glasses' is not distributed even once in the premises, no definite conclusion follows.

Some glasses are bowls. No bowl is a plate.

Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some glasses are not plates'.


5. 

Statements: Some trains are roads. No road is jungle. All flowers are jungles.

Conclusions:

  1. Some trains are flowers.
  2. Some trains are jungles.
  3. Some flowers are trains.
  4. No road is flower.

A. None follows
B. Only II follows
C. Only III follows
D. Only IV follows
E. All follow

Answer: Option D

Explanation:

Some trains are roads. No road is jungle.

Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some trains are not jungles'.

No road is jungle. All flowers are jungles.

Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, it follows that 'No flower is road'. IV is the converse of this conclusion and so it holds.

Some trains are roads, No flower is road.

As discussed above, it follows that 'Some trains are not flowers'.