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Standard XII

Mathematics

Fallacy

Statements: S...

Question

Statements: Some fishes are cats.
Some dogs are cats.
No fish is black.
Conclusions: I. No dog is black.
II. Some cats are black.

Only conclusion I follows.

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Only conclusion II follows.

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Either conclusion I or II follows.

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Neither conclusion I nor II follows.

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Solution

The correct option is D Neither conclusion I nor II follows.
Two cases are possible for this situation
Some dogs can be black.
So, conclusion I does not follow.
Some cats can be black, but not necessary.
So, conclusion II does not follow.
Thus, both conclusions are not true.

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Similar questions

Q. In the following question, two statements are given followed by four conclusions I, II, III and IV. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions if any follow from the given statements.

Statements
Some cats are dogs.
No dog is a toy.

Conclusions
I. Some dogs are cats.
II. Some toys are cats.
III. Some cats are not toys.
IV. All toys are cats.

Statements:

Some rats are cats.

All cats are bats.

Conclusions:

I. No rats are cats.

II. Some rats are bats.

Q. Statements are given followed by four conclusions. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions if any, follow the given statement.

Statements
Some cats are dogs.
Some dogs are stones.

Conclusions
I.No cat is a stone.
II. All dogs are stones.
III. Some stones are cats.
IV. No dog is a cat.

Statements

Some horses are tigers.

All tigers are goats.

All goats are dogs.

Some dogs are cats.

Conclusions

I. Some cats are horses.

II. Some dogs are tigers.

III. Some goats are horses.

IV. Some cats are tigers.

Statements:

Some horses are tigers.

All tigers are goats.

All goats are dogs.

Some dogs are cats.

Conclusions:

I. Some cats are horses.

II. Some dogs are tigers.

III. Some goats are horses.

IV. Some cats are tigers.

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Statements: Some fishes are cats. Some dogs are cats. No fish is black.Conclusions: I. No dog is black. II. Some cats are black.

The correct option is D Neither conclusion I nor II follows.Two cases are possible for this situationSome dogs can be black.So, conclusion I does not follow.Some cats can be black, but not necessary.So, conclusion II does not follow.Thus, both conclusions are not true.

Statements: Some fishes are cats.
Some dogs are cats.
No fish is black.
Conclusions: I. No dog is black.
II. Some cats are black.

The correct option is D Neither conclusion I nor II follows.
Two cases are possible for this situation
Some dogs can be black.
So, conclusion I does not follow.
Some cats can be black, but not necessary.
So, conclusion II does not follow.
Thus, both conclusions are not true.