Logical Reasoning - Logical Deduction

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

1. 

Statements:

All fruits are vegetables. All pens are vegetables. All vegetables are rains.

Conclusions:

  1. All fruits are rains.
  2. All pens are rains.
  3. Some rains are vegetables.

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

Answer: Option E

Explanation:

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

All fruits are vegetables. All vegetables are rains.

The conclusion must be universal affirmative and should not contain the middle term.

So, it follows that 'All fruits are rains'. Thus, I follows.

All pens are vegetables. All vegetables are rains.

Clearly, it follows that 'All pens are rains'. Thus, II follows.


2. 

Statements: Some towels are brushes. No brush is soap. All soaps are rats.

Conclusions:

  1. Some rats are brushes.
  2. No rat is brush.
  3. Some towels are soaps.

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

Answer: Option B

Explanation:

Some towels are brushes. No brush is soap.

Since one premise is particular and the other negative, the conclusion must be particular negative (O-type) and should not contain the middle term. So, it follows that 'Some towels are not soaps'. No brush is soap. All soaps are rats.

Since the middle term is distributed twice, the conclusion must be particular. Since one premise is negative, the conclusion must be negative. So, it follows that 'Some brushes are not rats'. Since I and II involve the same terms and form a complementary pair, so either I or II follows.


3. 

Statements: Some pictures are frames. Some frames are idols. All idols are curtains.

Conclusions:

  1. Some curtains are pictures.
  2. Some curtains are frames.
  3. Some idols are frames.

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

Answer: Option B

Explanation:

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

Some pictures are frames. Some frames are idols.

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

Some frames are idols. All idols are curtains.

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

Some pictures are frames. Some frames are curtains.

Since both the premises are particular, no definite conclusion can be drawn.


4. 

Statements: Some hills are rivers. Some rivers are deserts. All deserts are roads.

Conclusions:

  1. Some roads are rivers.
  2. Some roads are hills.
  3. Some deserts are hills.

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 hills are rivers. Some rivers are deserts.

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

Some rivers are deserts. All deserts are roads.

Since one premise is particular, the conclusion must be particular and shouldn't contain the middle term. So, it follows that 'Some rivers are roads'. I is the converse of this conclusion and so it holds.

Some hills are rivers. Some rivers are roads.

Again, since both the premises are particular, no definite conclusion follows.


5. 

Statements: Some saints are balls. All balls are bats. Some tigers are balls.

Conclusions:

  1. Some bats are tigers.
  2. Some saints are bats.
  3. All bats are balls.

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

Answer: Option A

Explanation:

Some saints are balls. All balls are bats.

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some saints are bats'. Thus, II follows. Some tigers are balls. All balls are bats.

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