Sure! Here are a few challenging questions related to determining the number of subsets in different sets.
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Question 1: If you have a set \( S = { a, b, c, d, e, f, g, h, i, j } \), how many subsets does this set have, including the empty set?
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Question 2: Consider the set \( T = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 } \). If you can only include even numbers in the subsets you count, how many unique subsets can you form?
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Question 3: Let \( U = { x_1, x_2, x_3, x_4, x_5 } \) be a set with 5 elements. If you must create subsets that contain at least 2 elements, how many such subsets can you have?
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Question 4: If you have a multiset \( M = { a, a, b, b, c } \) (where elements can repeat), how many distinct subsets does this multiset have?
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Question 5: Given a set \( R = { p, q, r, s } \), how many subsets can be formed such that at least one element is included from the original set?
Feel free to answer these or let me know if you would like additional questions or hints!