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

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Question: All cats are animals. Some animals 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 more information is provided

Correct Answer: Yes

Solution:

The conclusion follows logically from the premises. If all cats are animals and some animals are not dogs, it implies that there are cats that are not dogs.

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

Practice Questions

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

Questions & Step-by-Step Solutions

All cats are animals. Some animals are not dogs. Therefore, some cats are not dogs. Is this conclusion valid?
  • 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 certain animals that do not belong to the group of dogs.
  • Step 3: Combine the information: Since all cats are animals, and some animals are not dogs, it is possible that those animals that are not dogs include some cats.
  • Step 4: Draw the conclusion: Therefore, it is logical to say that some cats are not dogs because they fall into the category of animals that are not dogs.
  • Syllogism – A form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises).
  • Logical Validity – The property of an argument whereby if the premises are true, the conclusion must also be true.
  • Quantifiers – Understanding the use of 'all' and 'some' in logical statements and their implications.
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