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Which of the following statements about the 'Pigeonhole Principle' is true?

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Question: Which of the following statements about the \'Pigeonhole Principle\' is true?

Options:

  1. It applies only to finite sets.
  2. It guarantees at least one pair of identical items in a set.
  3. It is used to prove the existence of solutions in algebra.
  4. It is irrelevant in combinatorial problems.

Correct Answer: It guarantees at least one pair of identical items in a set.

Solution: 

The Pigeonhole Principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.

Which of the following statements about the 'Pigeonhole Principle' is true?

Practice Questions

Q1
Which of the following statements about the 'Pigeonhole Principle' is true?
  1. It applies only to finite sets.
  2. It guarantees at least one pair of identical items in a set.
  3. It is used to prove the existence of solutions in algebra.
  4. It is irrelevant in combinatorial problems.

Questions & Step-by-Step Solutions

Which of the following statements about the 'Pigeonhole Principle' is true?
  • Step 1: Understand what the Pigeonhole Principle is. It is a concept in mathematics.
  • Step 2: Identify the key components of the principle: 'n items' and 'm containers'.
  • Step 3: Recognize the condition: n (the number of items) must be greater than m (the number of containers).
  • Step 4: Conclude what the principle states: If you have more items than containers, at least one container will hold more than one item.
No concepts available.
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