A set of four elements has 24 subsets, since for every element there are two options: it may, or may not, be in a subset. This set of subsets includes the empty set and the original set, and everything in between.
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{1,2,4.7} is a proper subset of {1, 2, 3, 4, 4.7, 5}
Note that an empty set is included for the set of 11 numbers. That is 1 subset. Since order doesn't matter for this type of situation, we count the following number of subsets. 1-item subset: 11 choose 1 2-item subset: 11 choose 2 3-item subset: 11 choose 3 4-item subset: 11 choose 4 5-item subset: 11 choose 5 6-item subset: 11 choose 6 7-item subset: 11 choose 7 8-item subset: 11 choose 8 9-item subset: 11 choose 9 10-item subset: 11 choose 10 11-item subset: 11 choose 11 Note that the pattern of these values follows the Fibonacci sequence. If we add all of these values and 1 altogether, then you should get 2048 subsets that belong to the given set {1,2,3,4,5,6,7,8,9,10,11}. Instead of working out with cases, you use this form, which is 2ⁿ such that n is the number of items in the set. If there is 11 items in the set, then there are 211 possible subsets!
Let A be the set {1, 2, 3, 4}Let B be the set {1, 3}Let C be the set {1, 2, 4, 5}From this, we can say that B is a subset of A because all of the members of B are also members of A. In other words... B can be made up by selecting some of the pieces of A (in this case, 1 and 3). Note that C is not a subset of A because you cannot create C by selecting some parts of A. This is because C includes the number 5 and A doesn't.
There are 64 subsets, and they are:{}, {A}, {1}, {2}, {3}, {4}, {5}, {A,1}, {A,2}, {A,3}, {A,4}, {A,5}, {1,2}, {1,3}, {1,4}, {1,5}, {2,3}, {2,4}, {2,5}, {3,4}, {3, 5}, {4,5}, {A, 1, 2}, {A, 1, 3}, {A, 1, 4}, {A, 1, 5}, {A, 2, 3}, {A, 2, 4}, {A, 2, 5}, {A, 3, 4}, {A, 3, 5}, {A, 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}, {A, 1, 2, 3}, {A, 1, 2, 4}, {A, 1, 2, 5}, {A, 1, 3, 4}, {A, 1, 3, 5}, {A, 1, 4, 5}, {A, 2, 3, 4}, {A, 2, 3, 5}, {A, 2, 4, 5}, {A, 3, 4, 5}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {1, 3, 4, 5}, {2, 3, 4, 5}, {A, 1, 2, 3, 4}, {A, 1, 2, 3, 5}, {A, 1, 2, 4, 5}, {A, 1, 3, 4, 5}, {A, 2, 3, 4, 5}, {1, 2, 3, 4, 5} {A, 1, 2, 3,,4, 5} .