Logical Deduction - Section 2
Practice and master this topic with our carefully crafted questions.
In each of the following questions, two statements are given followed by three or four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some taxis have horns. Some taxis have lights.
Conclusions:
I. Every taxi has either horn or light.
II. Some taxis have neither light nor horn.
III. Some taxis have horns as well as lights.
IV. No taxi has horn as well as light.
Since both the premises are particular, no definite conclusion follows. However, III and IV form a complementary pair. Thus, either III or IV follows.
Statements: Some houses are offices. Some offices are schools.
Conclusions:
I. Some schools are houses.
II. Some offices are houses.
III. No house is school.
IV. Some schools are offices.
Since both the premises are particular, no definite conclusion follows. However, I and III involve only the extreme terms and form a complementary pair. So, either I or III follows. II is the converse of the first premise while IV is the converse of the second premise. Thus, both of them hold.
Statements: Some books are pens. No pen is pencil.
Conclusions:
I. Some pens are books.
II. Some pencils are books.
III. Some books are not pencils.
IV. All pencils are books.
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. Thus, III follows. I is the converse of the first premise and so it also holds.
Statements: All terrorists are guilty. All terrorists are criminals.
Conclusions:
I. Either all criminals are guilty or all guilty are criminals.
II. Some guilty persons are criminals.
III. Generally criminals are guilty.
IV. Crime and guilt go together.
Since the middle term 'terrorists' is distributed twice in the premises, the conclusion cannot be universal. So, it follows that 'Some guilty persons are criminals'. Thus, II holds.
Statements: Some tables are TVs. Some TVs are radios.
Conclusions:
I. Some tables are radios.
II. Some radios are tables.
III. All radios are TVs.
IV. All TVs are tables.
Since both the premises are particular, no definite conclusion follows.
Statements: Some bottles are drinks. All drinks are cups.
Conclusions:
I. Some bottles are cups.
II. Some cups are drinks.
III. All drinks are bottles.
IV. All cups are drinks.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some bottles are cups'. Thus, I follows. II is the converse of the second premise and so it also holds.
Statements: All branches are flowers. All flowers are leaves.
Conclusions:
I. All branches are leaves.
II. All leaves are branches.
III. All flowers are branches.
IV. Some leaves are branches.
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 branches are leaves'. Thus, I follows. IV is the converse of this conclusion and so it also holds.
Statements: Some bags are pockets. No pocket is a pouch.
Conclusions:
I. No bag is a pouch.
II. Some bags are not pouches.
III. Some pockets are bags.
IV. No pocket is a bag,
Since one premise is particular and the other negative, the conclusion must be particular negative and should not contain the middle term. So, II follows. III is the converse of the first premise and thus it also holds.
Statements: All aeroplanes are trains. Some trains are chairs.
Conclusions:
I. Some aeroplanes are chairs.
II. Some chairs are aeroplanes.
III. Some chairs are trains.
IV. Some trains are aeroplanes.
Since the middle term 'trains' is not distributed even once in the/premises, no definite conclusion follows. However, III is the converse of the second premise while IV is the converse of the first premise. So, both of them hold.
Statements: All politicians are honest. All honest are fair.
Conclusions:
I. Some honest are politicians.
II. No honest is politician.
III. Some fair are politicians.
IV. All fair are politicians.
Clearly, it follows that 'All politicians are fair'. I is the converse of the first premise, while III is the converse of the above conclusion. So, both I and III hold.