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$27$ persons attend a party. Which one of the following statements can never be true?

  1. There is a person in the party who is acquainted with all the $26$ members.
  2. Each person in the party has a different number of acquaintances.
  3. There is a person in the party who has odd number of acquaintances.
  4. In the party, there is no set of three mutual acquaintances. 
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