Statements: Some rats are cats. Some cats are dogs. No dog is cow.
Conclusions:
1. No cow is cat.
2. No dog is rat.
3. Some cats are rats.
Answer: D
Correct answer: Only (3)
Some rats are cats gives its converse, some cats are rats - conclusion 3. Conclusion 1 needs cows excluded from cats, whereas only dogs are excluded; and conclusion 2 crosses two particulars.
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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. Some lions are bats.
II. Some bats are cat.
Conclusion -
I. All lions are cat.
II. No cat are bats.
Answer: D
Correct answer: Neither I nor II follows
Both statements are particular - some lions are bats, some bats are cats - and a chain of “some” carries nothing along it. Conclusion I claims all lions are cats and conclusion II that no cat is a bat, and the second even contradicts what is given. Neither follows.
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Statements: All the research scholars are psychologists. Some psychologists are scientists.
Conclusions:
1. All the research scholars are scientists.
2. Some research scholars are scientists.
3. Some scientists are psychologists.
4. Some psychologists are research scholars.
Answer: A
Correct answer: Only (3) and (4)
Some psychologists are scientists gives its converse, some scientists are psychologists - conclusion 3; and all research scholars being psychologists gives some psychologists are research scholars, conclusion 4. Conclusions 1 and 2 need the psychologists who are scientists to be the research scholars, which is not given.
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Statements: All the bottles are boxes. All the boxes are bags. Some bags are trays.
Conclusions:
1. Some bottles are trays.
2. Some trays are boxes.
3. All the bottles are bags.
4. Some trays are bags.
Answer: A
Correct answer: Only (3) and (4)
All bottles are boxes and all boxes are bags, so all bottles are bags - conclusion 3. Some bags are trays gives its converse, some trays are bags - conclusion 4. Conclusions 1 and 2 need the bags that are trays to be bottles or boxes, which is not given.
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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.
A. An eagle lays eggs.
B. All birds lay eggs.
C. Some birds can fly.
D. An eagle cannot fly.
E. An eagle is a bird.
F. An eagle cannot swim.
Answer: B
Correct answer: BEA
Taking B and E as the premises: all birds lay eggs, and an eagle is a bird. It follows that an eagle lays eggs, which is A. The other segments - about flying and swimming - are neither needed nor derivable.
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Statements: All green are blue. All blue are white.
Conclusions:
1. Some blue are green.
2. Some white are green.
3. Some green are not white.
4. All white are blue.
Answer: A
Correct answer: Only (1) and (2)
All green are blue gives some blue are green, conclusion 1; and since all green are blue and all blue are white, all green are white, whence some white are green, conclusion 2. Conclusion 3 contradicts that, and conclusion 4 reverses a universal.
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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. No key is door.
II. All doors are pens.
III. Some pens are houses.
Conclusion -
I. No key is house.
II. Some pens are doors.
Answer: B
Correct answer: Only II follows
Conclusion II is simply the converse of the second statement: if all doors are pens then certainly some pens are doors. Conclusion I asks about keys and houses, and the statements link them only through pens - a middle term that is not distributed - so nothing follows there. Only II 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. All fruits are lions
II. All lions are foxes
III. Some foxes are beggars
Conclusion -
I. All fruits are foxes.
II. Some fruits are beggars.
Answer: A
Correct answer: Only I follows
All fruits are lions and all lions are foxes, so all fruits are foxes - conclusion I. Conclusion II asks about beggars, and we know only that some foxes are beggars; those need not be the fruits. Only I 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. Cars are birds.
B. Some birds are ants.
C. Cars are ants.
D. Some Cars are ants.
E. Some Cars are not ants.
F. No car is ant.
Answer: B
Correct answer: ADB
Taking A and D as the premises: cars are birds, and some cars are ants. Those cars are birds and they are ants, so some birds are ants, which is B. The premises must be the first two segments and the conclusion the third, and only this order works.
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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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