Statements:
I. No point is a brake.
II. No catch is a brake.
Conclusions:
I. Some points are not catches.
II. Some brakes are catches.
Answer: D
Correct answer: If neither conclusion I nor II follows
Both statements are negative - no point is a brake, no catch is a brake - and from two negatives nothing follows. Conclusion II even contradicts the second statement. Neither follows.
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In the question given below consists of five or six statements followed by options consisting of three statements put together in a specific order. Choose the option which indicates a valid argument containing logically related statements that is, where the third statement is conclusion drawn from preceding two statements.
Statement -
A. No apple is a door.
B. All poles are doors.
C. No pole is an apple.
D. Some poles are not apples.
E. Some apples are poles.
F. Some doors are not apples.
Answer: A
Correct answer: ABC
Taking A and B as the premises: no apple is a door, and all poles are doors. Anything that is a pole is therefore a door, and no door is an apple - so no pole is an apple, which is C. The other orders offered put a conclusion among the premises or draw more than the premises allow.
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Statements: Some cars are jeeps. All the boxes are jeeps. All the pens are cars.
Conclusions:
1. Some cars are boxes.
2. No pen is jeep.
3. Some boxes are cars.
Answer: A
Correct answer: None of three
Conclusions 1 and 3 link cars with boxes, which are joined only through jeeps as a predicate in both statements - an undistributed middle. Conclusion 2 denies any pen being a jeep, whereas all pens are cars and some cars are jeeps, so nothing of the kind follows. None of the three follows.
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Statements:
I. Some peace are wars.
II. No war is an alliance.
Conclusions:
I. No peace is alliance.
II. At least some peace are alliances.
Answer: C
Correct answer: If either conclusion I or II follows
Neither conclusion is established: the peace that are wars are certainly not alliances, but the rest of peace is left open, so we can say neither that no peace is an alliance nor that some are. The two between them, however, cover both possibilities, so either I or II must hold.
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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. All snakes are idiots.
II. Some idiots are people.
III. All people are soft.
Conclusion -
I. Some idiots are not snakes.
II. Some people are snakes.
III. Some soft are idiots.
Answer: C
Correct answer: Only III follows
Some idiots are people and all people are soft, so some idiots are soft - that is, some soft are idiots, conclusion III. Conclusion I asserts idiots who are not snakes, which need not exist, and conclusion II links people to snakes through a particular. Only III follows.
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Statements:
I. No rose is a lily.
II. Some lilies are lotuses.
Conclusions:
I. No rose is a lotus.
II. Some lotuses are not roses
Answer: B
Correct answer: If only conclusion II follows
The lilies that are lotuses are, by the first statement, not roses - so some lotuses are not roses, conclusion II. Conclusion I excludes all lotuses from roses, which does not follow. Only II follows.
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Statements: All cups are books. All books are shirts.
Conclusions:
1. Some cups are not shirts.
2. Some shirts are cups.
Answer: B
Correct answer: Only (2) conclusion follows
All cups are books and all books are shirts, so all cups are shirts - and therefore some shirts are cups, conclusion 2. Conclusion 1 says the opposite of what follows. Only 2 follows.
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Statements: All the actors are girls. All the girls are beautiful.
Conclusions:
1. All the actors are beautiful.
2. Some girls are actors.
Answer: D
Correct answer: Both (1) and (2) follow
All actors are girls and all girls are beautiful, so all actors are beautiful - conclusion 1. And all actors being girls gives its converse, some girls are actors - conclusion 2. Both follow.
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In 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 -
A. All cats are mad. All sick persons are mad. So, all sick persons are cats.
B. All oranges are white. All figs are oranges. So, all figs are white.
C. No man can crawl. No kite can crawl. So, all men are kites.
Answer: B
Correct answer: B
In B the reasoning runs through: all figs are oranges and all oranges are white, so all figs are white. A commits the same fault as before - cats and sick persons are both mad, which does not make them each other - and C draws a positive conclusion from two negative premises, which is never valid.
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Statements: Some pens are books. Some books are pencils.
Conclusions:
1. Some pens are pencils.
2. Some pencils are pens.
3. All pencils are pens.
4. All books are pens.
Answer: D
Correct answer: None of the four
Both statements are particular, and the books that are pens need not be the books that are pencils, so nothing links pens to pencils. Conclusions 3 and 4 make universals out of particulars. None of the four follows.
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