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If the first two statements are true, is the final statement true? 'All cats are

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Question: If the first two statements are true, is the final statement true? \'All cats are animals. Some animals are dogs. Therefore, some cats are dogs.\'

Options:

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

Correct Answer: False

Solution: 

The conclusion does not logically follow from the premises.

If the first two statements are true, is the final statement true? 'All cats are

Practice Questions

Q1
If the first two statements are true, is the final statement true? 'All cats are animals. Some animals are dogs. Therefore, some cats are 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? 'All cats are animals. Some animals are dogs. Therefore, some cats are 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 dogs.' This means there are some animals that are dogs, but not all animals are dogs.
  • Step 3: Analyze the conclusion: 'Therefore, some cats are dogs.' This suggests that there are cats that are also dogs.
  • Step 4: Check if the conclusion logically follows from the first two statements. Since all cats are animals and only some animals are dogs, it does not mean that any cats are dogs.
  • Step 5: Conclude that the final statement is not true based on the information given in the first two statements.
  • Logical Deduction – The ability to derive a conclusion from given premises using valid reasoning.
  • Syllogism – A form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises).
  • Quantifiers in Logic – Understanding the implications of universal ('all') and particular ('some') quantifiers in logical statements.
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