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All cats are mammals. Some mammals are not dogs. Therefore, some cats are not do

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Question: All cats are mammals. Some mammals are not dogs. Therefore, some cats are not dogs. Is this conclusion valid?

Options:

  1. Yes
  2. No
  3. Cannot be determined
  4. Only if all mammals are cats

Correct Answer: Yes

Solution: 

The conclusion is valid because if all cats are mammals and some mammals are not dogs, it follows that some cats (which are mammals) are not dogs.

All cats are mammals. Some mammals are not dogs. Therefore, some cats are not do

Practice Questions

Q1
All cats are mammals. Some mammals are not dogs. Therefore, some cats are not dogs. Is this conclusion valid?
  1. Yes
  2. No
  3. Cannot be determined
  4. Only if all mammals are cats

Questions & Step-by-Step Solutions

All cats are mammals. Some mammals are not dogs. Therefore, some cats are not dogs. Is this conclusion valid?
  • 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, 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 logically follows that some cats are not dogs.
  • Logical Deduction – The ability to draw conclusions based on given premises.
  • Syllogism – A form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises).
  • Categorical Logic – Understanding relationships between categories (e.g., all, some) in logical statements.
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