R. S. Aggarwal Solutions for Chapter: Logic, Exercise 2: EXERCISE

In the question given below, two statements P and Q are given. Look into their logical acceptability and mark the correct answer.

P: All A's are B's. Some B's are C's. Therefore, some A's are C's.

Q: Some A's are B's. All C's are A's. Therefore, some C's are B's.

The question given below consists of 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, i.e. where the third statement is a conclusion drawn from the preceding two statements.

A: Aardvarks need sleep.

B: All animals need sleep.

C: Dogs are animals.

D: Some dogs need sleep.

E: Aardvarks are animals.

F: Some aardvarks are dogs.

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 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?