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How many non-empty subsets of {1, 2, 3, 4, 5} consist entirely of prime numbers? (We form a subset of the group of numbers by choosing some number of them, without regard to order. So, {1, 2, 3} is the same as {3, 1, 2}.)

 Jan 1, 2022
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∅ | {1} | {2} | {3} | {4} | {5} | {1, 2} | {1, 3} | {1, 4} | {1, 5} | {2, 3} | {2, 4} | {2, 5} | {3, 4} | {3, 5} | {4, 5} | {1, 2, 3} | {1, 2, 4} | {1, 2, 5} | {1, 3, 4} | {1, 3, 5} | {1, 4, 5} | {2, 3, 4} | {2, 3, 5} | {2, 4, 5} | {3, 4, 5} | {1, 2, 3, 4} | {1, 2, 3, 5} | {1, 2, 4, 5} | {1, 3, 4, 5} | {2, 3, 4, 5} | {1, 2, 3, 4, 5} (total: 32)

 

7 without regard to size.

 Jan 1, 2022

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