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Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be the power set of D ,...

  1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be the power set of D , i.e. the set of all subsets of D .
  1. How many elements are there in P(D) ? Prove it!
  1. Which number is greater: the number of different subsets of D which contain the digit 7 or the number of different subsets of D which do not contain the digit 7? Explain why!

  1. Which number is greater: the number of different subsets of D which contain more than five digits from D (like {0,1,2,5,7,9} or D itself) or the number of different subsets of D which contain less than five digits from D (like {3,4,6,8} or )? Explain why!

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