The question below is based on a set of given propositions I to IV. Select the best answer.

I: All P are Q.

II: Some P are not Q.

III: Some, but not all, P are Q.

IV: No P is Q.

Considered only by themselves, which of the following pairs of statements might both be false but could not both be true?

The question below is based on a set of given propositions I to IV. Select the best answer.

I: All P are Q.

II: Some P are not Q.

III: Some, but not all, P are Q.

IV: No P is Q.

Which of the following pairs of statements considered by themselves cannot be both true and cannot be both false?

The question below is based on a set of given propositions I to IV. Select the best answer.

I: All P are Q.

II: Some P are not Q.

III: Some, but not all, P are Q.

IV: No P is Q.

Which of the following correctly describes the relationships among the above statements?

Examine the given statements carefully and find out which two of the statements can not be true simultaneously, but can both be false.

1. All animals are carnivorous.

2. Some animals are not carnivorous.

3. Animals are not carnivorous.

4. Some animals are carnivorous.

Examine the given statements carefully and find out which two of the statements can not be true simultaneously, but can both be false.

1. All children are inquisitive.

2. Some children are inquisitive.

3. No children are inquisitive.

4. Some children are not inquisitive.

Examine the given statements carefully and find out which two of the statements can not be true simultaneously, but can both be false.

1. Some nations wish for peaceful coexistence.

2. All nations wish for peaceful coexistence.

3. Some nations are not wishing for peaceful coexistence.

4. No nations are wishing for peaceful coexistence.

Examine the following statements regarding a set of balls.

1. All balls are black.

2. All balls are white.

3. Only some balls are black.

4. No balls are black.

Assuming that the balls can only be black or white, which of the two statements given above can both be true and both be false?

Directions: In the question below are given three statements followed by three conclusions numbered I, II, and III. You have to take the given statements to be true even if they seem to be at variance from the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements: All dolls are windows. All bottles are windows. All cars are bottles.

Conclusions:

I. All cars are windows.

II. Some cars are dolls.

III. Some windows are cars.

Directions: In the question below are given three statements followed by three conclusions numbered I, II, and III. You have to take the given statements to be true even if they seem to be at variance from the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements: All fruits are vegetables. All pens are vegetables. All vegetables are rains.

Conclusions:

I. All fruits are rains.
II. All pens are rains.
III. Some rains are vegetables.