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All dogs are pets. Some pets are not cats. Therefore, some dogs are not cats. Is

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

Options:

  1. Yes
  2. No
  3. Only if more information is provided
  4. Cannot be determined

Correct Answer: No

Solution: 

The conclusion is not necessarily valid. Just because some pets are not cats does not imply that some dogs are not cats.

All dogs are pets. Some pets are not cats. Therefore, some dogs are not cats. Is

Practice Questions

Q1
All dogs are pets. Some pets are not cats. Therefore, some dogs are not cats. Is this conclusion valid?
  1. Yes
  2. No
  3. Only if more information is provided
  4. Cannot be determined

Questions & Step-by-Step Solutions

All dogs are pets. Some pets are not cats. Therefore, some dogs are not cats. Is this conclusion valid?
  • Step 1: Understand that all dogs are included in the category of pets.
  • Step 2: Recognize that some pets are not cats, which means there are pets that are neither dogs nor cats.
  • Step 3: Realize that just because some pets are not cats, it does not mean that those pets are dogs.
  • Step 4: Conclude that the statement 'some dogs are not cats' cannot be confirmed just from the information given.
  • Logical Reasoning – The question tests the ability to analyze syllogistic reasoning and understand the relationships between categories.
  • Quantifiers in Logic – The use of quantifiers like 'all' and 'some' is crucial in determining the validity of the conclusion.
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