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

Practice Questions

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

Questions & Step-by-Step Solutions

If all cats are animals and some animals are not dogs, can we conclude that some cats are not dogs?
Correct Answer: Yes
  • Step 1: Understand that all cats belong to the group of animals.
  • Step 2: Recognize that within the group of animals, there are some that are not dogs.
  • Step 3: Since all cats are animals, some of those cats must also be part of the animals that are not dogs.
  • Step 4: Therefore, we can conclude 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.
  • Quantifiers in Logic – Understanding the implications of universal and existential quantifiers (e.g., 'all', 'some').
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