Logical Deduction - Section 1
Practice and master this topic with our carefully crafted questions.
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.
Statements: All cars are cats. All fans are cats.
Conclusions:
I. All cars are fans
II. Some fans are cars.
Since the middle term 'cats' is not distributed even once in the premises, no definite conclusion follows.
Statements: All young scientists are open-minded. No open-minded men are superstitious.
Conclusions:
I. No scientist is superstitious.
II. No young people are superstitious.
The subject in both the conclusions is vague. The true conclusion is 'No young scientist is superstitious'. Thus, neither I nor II follows.
Statements: Some pastries are toffees. All toffees are chocolates.
Conclusions:
I. Some chocolates are toffees.
II. Some toffees are not pastries.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. Thus, it follows that 'Some pastries are chocolates', I is the converse of the second premise and so it holds. Since both the premises are affirmative, the conclusion cannot be negative. Thus, II does not follow.
Statements: All boys are honest. Sachin is honest.
Conclusions:
I. Sachin is a boy.
II. All honest persons are boys.
Both the premises are A type propositions. So, the middle term 'honest' forming the predicate in each is not distributed in either. Since the middle term is not distributed even once, no definite conclusion follows.
Statements: All pens are roads. All roads are houses.
Conclusions:
I. All houses are pens.
II. Some houses are pens.
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 pens are houses'. II is the converse of this conclusion and so it holds. Since the term 'houses' is distributed in I without being distributed in any of the premises, so I does not follow.
Statements: All artists are smokers. Some smokers are drunkards.
Conclusions:
I. All smokers are artists.
II. Some drunkards are not smokers.
Since the middle term 'smokers' is not distributed even once in the premises, no definite conclusion follows.
Statements: All fish are tortoise. No tortoise is a crocodile.
Conclusions:
I. No crocodile is a fish.
II. No fish is a crocodile.
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.
Statements: Some dedicated souls are angels. All social workers are angels.
Conclusions:
I. Some dedicated souls are social workers.
II. Some social workers are dedicated souls.
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.
Statements: No gentleman is poor. All gentlemen are rich.
Conclusions:
I. No poor man is rich.
II. No rich man is poor.
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.
Statements: Some swords are sharp. All swords are rusty
Conclusions:
I. Some rusty things are sharp.
II. Some rusty things are not sharp.
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.