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All dogs are animals. Some animals are not pets. Therefore, some dogs are not pe

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

Options:

  1. Yes
  2. No
  3. Only if all animals are dogs
  4. Only if some pets are not animals

Correct Answer: No

Solution: 

The conclusion is not valid because while all dogs are animals, it does not imply that some dogs are not pets since all dogs could potentially be pets.

All dogs are animals. Some animals are not pets. Therefore, some dogs are not pe

Practice Questions

Q1
All dogs are animals. Some animals are not pets. Therefore, some dogs are not pets. Is this conclusion valid?
  1. Yes
  2. No
  3. Only if all animals are dogs
  4. Only if some pets are not animals

Questions & Step-by-Step Solutions

All dogs are animals. Some animals are not pets. Therefore, some dogs are not pets. Is this conclusion valid?
  • Step 1: Understand that all dogs belong to the category of animals.
  • Step 2: Recognize that some animals do not fall into the category of pets.
  • Step 3: Note that just because some animals are not pets, it does not mean that any specific group of animals (like dogs) must also not be pets.
  • Step 4: Realize that all dogs could still be pets, even if some other animals are not.
  • Step 5: Conclude that the statement 'some dogs are not pets' is not necessarily true based on 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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