Statements:
I. Some rulers are dancers.
II. All dancers are short.
Conclusions:
I. Some rulers are short.
II. All rulers are short.
Answer: A
Correct answer: If only conclusion I follows
Some rulers are dancers and all dancers are short, so those rulers are short - some rulers are short, conclusion I. Conclusion II makes it all rulers, which a particular statement cannot support. Only I follows.
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Statements: All the books are papers. Some papers are journals. Some journals are calendars.
Conclusions:
1. Some journals are books.
2. Some calendars are papers.
3. Some books are journals.
4. Some books are calendars.
Answer: D
Correct answer: None of the four
The chain runs books → papers by a universal, but from papers onward it is all particulars - some papers are journals, some journals are calendars - and those need not be the same papers or journals. None of the four follows.
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The question given below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.
Statement -
I. Some guns are hammers.
II. Some hammers are bullets.
III. Some bullets are axes.
Conclusion -
I. Some axes are hammers.
II. Some bullets are guns.
III. Some axes are guns
Answer: D
Correct answer: None follows
All three statements are particular - some guns are hammers, some hammers are bullets, some bullets are axes - and a chain of “some” carries nothing along it. None follows.
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Statements: All the books are pencils. No pencil is eraser.
Conclusions:
1. All the pencils are books.
2. Some erasers are books.
3. No book is eraser.
4. Some books are erasers.
Answer: A
Correct answer: Only (3)
All books are pencils and no pencil is an eraser, so nothing that is a book can be an eraser - no book is an eraser, conclusion 3. Conclusions 2 and 4 assert the opposite, and conclusion 1 reverses a universal.
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Statements:
I. Some students are bad.
II. Some bad are good.
Conclusions:
I. Some students are good.
II. All good are bad.
Answer: D
Correct answer: If neither conclusion I nor II follows
Both statements are particular, and the bad who are students need not be the bad who are good, so nothing links students to good. Conclusion II makes a universal out of a particular. Neither follows.
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In the question below is given a statement followed by two conclusions numbered I and II.
Give answer
(A) If only I follows
(B) If only II follows
(C) If either I or II follows
(D) If neither I nor II follows
(E) If both I and II follow.
Statement -
I. All dogs are cats.
II. All rats are cats.
Conclusion -
I. No dogs are cat.
II. Some cat are rat.
Answer: B
Correct answer: Only II follows
All rats are cats, so its converse holds: some cats are rats - conclusion II. Conclusion I contradicts the first statement, which says all dogs are cats. Only II follows.
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Statements: All the harmoniums are instruments. All the instruments are flutes.
Conclusions:
1. All the flutes are instruments.
2. All the harmoniums are flutes.
Answer: B
Correct answer: Only (2) conclusion follows
All harmoniums are instruments and all instruments are flutes, so all harmoniums are flutes - conclusion 2. Conclusion 1 reverses a universal: all instruments being flutes does not make all flutes instruments. Only 2 follows.
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Statements: Some papers are pens. All the pencils are pens.
Conclusions:
1. Some pens are pencils.
2. Some pens are papers.
Answer: D
Correct answer: Both (1) and (2) follow
All pencils are pens gives its converse, some pens are pencils - conclusion 1. And some papers being pens gives some pens are papers - conclusion 2. Both follow.
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In the question below has a set of three or four statements. Each set of statements is further divided into three segments. Choose the alternative where the third segment in the statement can be logically deduced using both the preceding two, but not just from one of them.
Statement -
A. All ugly things are happy. She is ugly. She is happy.
B. All nice things are flat. TVs are flat. TVs are nice things.
C. Potatoes are balls. All balls are fruits. Potatoes are fruits.
Answer: D
Correct answer: A and C
In A the conclusion follows: all ugly things are happy and she is ugly, so she is happy. In C it follows as well: potatoes are balls and all balls are fruits, so potatoes are fruits. B is the familiar fault - nice things are flat and TVs are flat, which does not make TVs nice.
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Statements: Some envelops are gums. Some gums are seals. Some seals are adhesives.
Conclusions:
1. Some envelopes are seals.
2. Some gums are adhesives.
3. Some adhesives are seals.
4. Some adhesives are gums.
Answer: A
Correct answer: Only (3)
Some seals are adhesives gives its converse, some adhesives are seals - conclusion 3. Every other conclusion has to cross two particular statements, and the middle terms in them need not be the same things.
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