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

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

Options:

  1. A. All cats are dogs.
  2. B. Some cats are not dogs.
  3. C. All mammals are cats.
  4. D. No mammals are cats.

Correct Answer: B. Some cats are not dogs.

Solution: 

Since some mammals are not dogs and all cats are mammals, it follows that some cats must not be dogs.

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

Practice Questions

Q1
If all cats are mammals and some mammals are not dogs, which of the following must be true?
  1. A. All cats are dogs.
  2. B. Some cats are not dogs.
  3. C. All mammals are cats.
  4. D. No mammals are cats.

Questions & Step-by-Step Solutions

If all cats are mammals and some mammals are not dogs, which of the following must be true?
  • Step 1: Understand that all cats belong to the group called mammals.
  • Step 2: Recognize that there is a group of mammals that are not dogs.
  • Step 3: Since all cats are mammals, they are included in the group of mammals.
  • Step 4: If some mammals are not dogs, then it is possible that some of those mammals could be cats.
  • Step 5: Therefore, 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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