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If the first two statements are true, is the final statement true? 1. All cats a

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Question: If the first two statements are true, is the final statement true? 1. All cats are animals. 2. Some animals are not dogs. 3. Therefore, some cats are not dogs.

Options:

  1. True
  2. False
  3. Cannot be determined
  4. None of the above

Correct Answer: Cannot be determined

Solution: 

The conclusion cannot be definitively drawn from the premises provided.

If the first two statements are true, is the final statement true? 1. All cats a

Practice Questions

Q1
If the first two statements are true, is the final statement true? 1. All cats are animals. 2. Some animals are not dogs. 3. Therefore, some cats are not dogs.
  1. True
  2. False
  3. Cannot be determined
  4. None of the above

Questions & Step-by-Step Solutions

If the first two statements are true, is the final statement true? 1. All cats are animals. 2. Some animals are not dogs. 3. Therefore, some cats are not dogs.
  • Step 1: Understand the first statement: 'All cats are animals.' This means every cat belongs to the group of animals.
  • Step 2: Understand the second statement: 'Some animals are not dogs.' This means there are animals that are not part of the dog group.
  • Step 3: Analyze the conclusion: 'Therefore, some cats are not dogs.' We need to see if this can be true based on the first two statements.
  • Step 4: Since all cats are animals, and some animals are not dogs, it is possible that some of those animals that are not dogs could be cats.
  • Step 5: However, we cannot be sure that any specific cat is not a dog because we don't know if those non-dog animals include cats or not.
  • Step 6: Therefore, we cannot definitively conclude that some cats are not dogs based on the information given.
  • Logical Deduction – The ability to infer conclusions from given premises.
  • Categorical Logic – Understanding relationships between categories (e.g., all, some, none).
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