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If all cats are mammals and some mammals are not pets, can we conclude that some

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Question: If all cats are mammals and some mammals are not pets, can we conclude that some cats are not pets?

Options:

  1. Yes, definitely.
  2. No, not necessarily.
  3. Only if all mammals are cats.
  4. Only if some cats are not mammals.

Correct Answer: No, not necessarily.

Solution: 

The conclusion cannot be drawn because while some mammals are not pets, it does not specify that those mammals are cats.

If all cats are mammals and some mammals are not pets, can we conclude that some

Practice Questions

Q1
If all cats are mammals and some mammals are not pets, can we conclude that some cats are not pets?
  1. Yes, definitely.
  2. No, not necessarily.
  3. Only if all mammals are cats.
  4. Only if some cats are not mammals.

Questions & Step-by-Step Solutions

If all cats are mammals and some mammals are not pets, can we conclude that some cats are not pets?
  • Step 1: Understand that all cats belong to the group of mammals.
  • Step 2: Recognize that some mammals do not fall into the category of pets.
  • Step 3: Note that the statement about mammals not being pets does not specify that these mammals are cats.
  • Step 4: Conclude that we cannot assume any of the non-pet mammals are cats, so we cannot say that some cats are not pets.
  • Logical Deduction – The ability to draw conclusions based on given premises and understand the relationships between different categories.
  • Categorical Logic – Understanding the relationships between different groups, such as 'all', 'some', and 'none', in logical statements.
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