Logical Deduction - 01

01. Statements : All jungles are buses. All books are buses. All fruits are books.

Conclusions :
I. >Some fruits are jungles.
II. Some buses are books.
III. Some buses are jungles.
IV. All fruits are buses.

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

Solution:
III is the converse of the first premise and II is the converse of the second premise.

So, both of them hold.

All fruits are books. All books are buses.

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 fruits are buses'. Thus, IV follows.

All jungles are buses. All books are buses.

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

All fruits are buses. All books are buses.

As discussed above, no definite conclusion can be drawn.

All jungles are buses. All fruits are buses.

Again, no definite conclusion follows.

02. Statements : No table is fruit. No fruit is window. All windows are chairs.

Conclusions :
I. No window is table.
II. No chair is fruit.
III. No chair is table.
IV. All chairs are windows.

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

Solution:
No table is fruit. No fruit is window.

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

No fruit is window. All windows are chairs.

Since the middle term 'windows' is distributed twice and one premise is negative, the conclusion must be particular negative. So, it follows that 'Some chairs are not fruits'.

03. Statements : Some tapes are discs. Some discs are cassettes. Some cassettes are songs.

Conclusions :
I. Some songs are discs.
II. Some cassettes are tapes.
III. Some songs are tapes.
IV. No song is a disc.

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

Solution:
Since each combination of premises shall contain two particular premises, no definite conclusion can be drawn. However, I and IV involve the extreme terms of the second and third premises and form a complementary pair. Thus, either I or IV follows.

04. Statements : Some papers are cats. All cats are bats. No bat is horse.

Conclusions :
I. Some papers are horses.
II. No horse is cat.
III. Some bats are papers.
IV. All papers are bats.

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

Solution:
Some papers are cats. All cats are bats.

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

All cats are bats. No bat is horse.

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 cat is horse'. II is the converse of this conclusion and so it holds.

Some papers are bats. No bat is horse.

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 papers are not horses'.

05. Statements : No man is sky. No sky is road. Some men are roads.

Conclusions :
I. No road is man.
II. No road is sky.
III. Some skies are men.
IV. All roads are men.

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

Solution:
II is the converse of the second premise and so it holds.

No man is sky. No sky is road.

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

No man is sky. Some men are roads.

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 roads are not skies'.

No sky is road. Some men are roads.

As discussed above, it follows that 'Some men are not skies'.

Hence, only II follows.

06. Statements : No paper is pen. No pen is pencil. All erasers are papers.

Conclusions :
I. Some papers are erasers.
II. No pencil is eraser.
III. No pen is eraser.
IV. All papers are erasers.

  • 1Only I and II follow
  • 2Only II and III follow
  • 3Only I, II and III follow
  • 4None of these
Answer:- 1
Explanation:-

Solution:
I is the converse of the third premise and so it holds.

No paper is pen. No pen is pencil.

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

All erasers are papers. No paper is pen.

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 eraser is pen'. III is the converse of this conclusion and so it holds.

Hence, only I and III follow.

07. Statements : All myths are fictions. No fiction is novel. All novels are stories.

Conclusions :
I. No myth is novel.
II. Some fictions are novels.
III. Some fictions are myths.
IV. Some myths are novels.

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

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

All myths are fictions. No fiction is novel.

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 myth is novel'. Thus, I follows.

No fiction is novel. All novels are stories.

Since the middle term 'novels' is distributed twice in the premises, the conclusion must be particular. Since one premise is negative, the conclusion must be negative.

So, it follows that 'Some stories are not fictions'.

Hence, only I and III follow.

08. Statements : All rods are bricks. Some bricks are ropes. All ropes are doors.
Conclusions :
I. Some rods are doors.
II. Some doors are bricks. III. Some rods are not doors.
IV. All doors are ropes.

  • 1Only I and II follow
  • 2Only I, II and III follow
  • 3Only either I or III, and II follow
  • 4None of these
Answer:- 1
Explanation:-

Solution:
All rods are bricks. Some bricks are ropes.

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

Some bricks are ropes. All ropes are doors.

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

All rods are bricks. Some bricks are doors.

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

However, I and III involve the extreme terms. But, since they are not contradictory, they do not form a complementary pair.

Hence, only II follows.

09. Statements : No house is school. All colleges are schools. All schools are teachers.

Conclusions :
I. No house is teacher.
II. All colleges are teachers.
III. Some teachers are not houses.
IV. No college is house.

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

Solution:
All colleges are schools. No house is school.

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 college is house'. Thus, IV follows.

All colleges are schools. All schools are teachers.

Clearly, it follows that 'All colleges are teachers'. Thus, II follows.

No house is school. All schools are teachers.

Since the middle term 'schools' is distributed twice, the conclusion must be particular.

Since one premise is negative, the conclusion must be negative. So, it follows that 'Some teachers are not houses'.

10. Statements : All needles are threads. All threads are boxes. All trees are boxes.

Conclusions :
I. No needle is tree.
II. Some trees are threads.
III. Some boxes are needles.
IV. Some trees are needles.

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

Solution:
All needles are threads. All threads are boxes.

Since both the premises are universal and affirmative, the conclusion must be universal affirmative (A-type) and should not contain the middle term. So, it follows that 'All needles are boxes'. III is the converse of this conclusion and so it holds.

All threads are boxes. All trees are boxes.

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

All needles are boxes. All trees are boxes.

Again, since the middle term 'boxes' is not distributed even once in the premises, no definite conclusion can be drawn. However, I and IV involve the extreme terms of these two statements and form a complementary pair. Thus, either I or IV follows.

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