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

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

Options:

  1. Yes
  2. No
  3. Cannot be determined
  4. All cats are dogs

Correct Answer: Cannot be determined

Solution:

The information does not allow us to conclude that some cats are not dogs, as the relationship is not definitive.

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

Practice Questions

Q1
If all cats are mammals and some mammals are not dogs, can we conclude that some cats are not dogs?
  1. Yes
  2. No
  3. Cannot be determined
  4. All cats are dogs

Questions & Step-by-Step Solutions

If all cats are mammals and some mammals are not dogs, can we conclude that some cats are not dogs?
  • Step 1: Understand that all cats belong to the group of mammals.
  • Step 2: Recognize that some mammals are not dogs, meaning there are mammals that do not belong to the dog group.
  • Step 3: Realize that while all cats are mammals, we do not know if those specific cats are part of the mammals that are not dogs.
  • Step 4: Conclude that we cannot definitively say that some cats are not dogs based on the information given.
  • 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 (e.g., all, some) and how they interact.
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