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If all cats are mammals and some mammals are not dogs, which of the following st

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Question: If all cats are mammals and some mammals are not dogs, which of the following statements must be true?

Options:

  1. All cats are dogs.
  2. Some cats are not dogs.
  3. All mammals are cats.
  4. Some dogs are not mammals.

Correct Answer: Some cats are not dogs.

Solution: 

Since not all mammals are dogs, it follows that some cats, being mammals, cannot be dogs.

If all cats are mammals and some mammals are not dogs, which of the following st

Practice Questions

Q1
If all cats are mammals and some mammals are not dogs, which of the following statements must be true?
  1. All cats are dogs.
  2. Some cats are not dogs.
  3. All mammals are cats.
  4. Some dogs are not mammals.

Questions & Step-by-Step Solutions

If all cats are mammals and some mammals are not dogs, which of the following statements must be true?
  • Step 1: Understand that all cats belong to the group of mammals.
  • Step 2: Recognize that some mammals do not belong to the group of dogs.
  • Step 3: Since all cats are mammals, if some mammals are not dogs, it means that at least some cats cannot be dogs.
  • Step 4: Conclude that it must be true that some cats are not dogs.
  • Logical Deduction – The ability to draw conclusions based on given premises.
  • Categorical Logic – Understanding relationships between categories (e.g., all, some) in logical statements.
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