logical deduction logical 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.

6.

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 & Explanation

Answer: Option A

Explanation:

Since both the premises are particular, no definite conclusion follows.
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7.

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 & Explanation

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.
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8.

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 & Explanation

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.
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9.

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 & Explanation

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.
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10.

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 & Explanation

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.