Logical Deduction - Section 2 (1)

Directions to Solve

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:

Every taxi has either horn or light.

Some taxis have neither light nor horn.

Some taxis have horns as well as lights.

No taxi has horn as well as light.

A.	Only I and II follow
B.	Only II and III follow
C.	Only II and IV follow
D.	Either III or IV follows
E.	All follow

Answer: Option D

Explanation:

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:

Some schools are houses.

Some offices are houses.

No house is school.

Some schools are offices.

A.	Only II and III follow
B.	Only I and IV follow
C.	Only either III or IV, and I follow
D.	Only II and IV and either I or III follow.

Answer: Option D

Explanation:

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 bottles are drinks. All drinks are cups.

Conclusions:

Some bottles are cups.

Some cups are drinks.

All drinks are bottles.

All cups are drinks.

A.	Only I and II follow
B.	Only II and III follow
C.	Only II and IV follow
D.	Only III and IV follow
E.	Only I and IV follow

Answer: Option A

Explanation:

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: Some books are pens. No pen is pencil.

Conclusions:

Some pens are books.

Some pencils are books.

Some books are not pencils.

All pencils are books.

A.	Only I follows
B.	Only II and III follow
C.	Only I and III follow
D.	Only I and II follow

Answer: Option C

Explanation:

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:

Either all criminals are guilty or all guilty are criminals.

Some guilty persons are criminals.

Generally criminals are guilty.

Crime and guilt go together.

A.	Only I follows
B.	Only I and III follow
C.	Only II follows
D.	Only II and IV follow

Answer: Option C

Explanation:

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:

Some tables are radios.

Some radios are tables.

All radios are TVs

All TVs are tables.

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

Answer: Option A

Explanation:

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

Statements: Some clothes are marbles. Some marbles are bags.

Conclusions:

No cloth is a bag.

All marbles are bags.

Some bags are clothes

No marble is a cloth.

A.	Only either I or IV follows
B.	Only either I or II follows
C.	None follows
D.	Only either I or III follows

Answer: Option D

Explanation:

Since both the premises are particular, no definite conclusion follows. However, I and III involve only the extreme terms and form a complementary pair. Thus, either I or III follows.

Statements: All politicians are honest. All honest are fair.

Conclusions:

Some honest are politicians.

No honest is politician.

Some fair are politicians.

All fair are politicians.

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

Answer: Option D

Explanation:

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.

Logical Deduction - Section 2 (1)

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