Logical Deduction

[abdulsaboor]

Logical Deduction

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

Give answer:

(A) If only conclusion I follows
(B) If only conclusion II follows
(C) If either I or II follows
(D) If neither I nor II follows and
(E) If both I and II follow.

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1.
Statements: No women teacher can play. Some women teachers are athletes.

Conclusions:

Male athletes can play.
Some athletes can play.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow


Explanation:

Since one premise is negative, the conclusion must be negative. So, neither conclusion follows.

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2.
Statements: All bags are cakes. All lamps are cakes.

Conclusions:

Some lamps are bags.
No lamp is bag.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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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3.
Statements: All mangoes are golden in colour. No golden-coloured things are cheap.

Conclusions:

All mangoes are cheap.
Golden-coloured mangoes are not cheap.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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.

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4.
Statements: Some kings are queens. All queens are beautiful.

Conclusions:

All kings are beautiful.
All queens are kings.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

Since one premise is particular, the conclusion must be particular. So, neither I nor II follows.

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5.
Statements: Some doctors are fools. Some fools are rich.

Conclusions:

Some doctors are rich
Some rich are doctors.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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

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6.
Statements: All roads are waters. Some waters are boats.

Conclusions:

Some boats are roads.
All waters are boats.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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.

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7.
Statements: No bat is ball. No ball is wicket.

Conclusions:

No bat is wicket.
All wickets are bats.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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

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8.
Statements: All flowers are trees. No fruit is tree.

Conclusions:

No fruit is flower.
Some trees are flowers.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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.

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9.
Statements: Every minister is a student. Every student is inexperienced.

Conclusions:

Every minister is inexperienced.
Some inexperienced are students.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

'Every' is equivalent to 'All'. Thus, since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, I follows. II is the converse of the second premise and thus it also holds.

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10.
Statements: All roads are poles. No pole is a house.

Conclusions:

Some roads are houses.
Some houses are poles.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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

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11.
Statements: All fish are tortoise. No tortoise is a crocodile.

Conclusions:

No crocodile is a fish.
No fish is a crocodile.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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.

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12.
Statements: Some dedicated souls are angels. All social workers are angels.

Conclusions:

Some dedicated souls are social workers.
Some social workers are dedicated souls.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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.

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13.
Statements: No gentleman is poor. All gentlemen are rich.

Conclusions:

No poor man is rich.
No rich man is poor.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

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.

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14.
Statements: Some swords are sharp. All swords are rusty

Conclusions:

Some rusty things are sharp.
Some rusty things are not sharp.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, I follows. Since both the premises are affirmative, the conclusion cannot be negative. Thus, II does not follow.

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15.
Statements: All fishes are grey in colour. Some fishes are heavy.

Conclusions:

All heavy fishes are grey in colour.
All light fishes are not grey in colour.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow

Explanation:

Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some heavy things are grey in colour'. I is a cumulative result of this conclusion and the first premise. Thus, only I holds.