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Is there any formula that can tell you the number of all possible subsets of a set?

  • I'm doing my Math Homework, and there is this question, "Write down all possible subsets of the following set: A = (1,2,3,4)" Now I've got my answer, but I need to confirm it. And to confirm it, I need to know what is the maximum number of subsets that can be made from the set A. So, is there any formula that can help me get that number???? I checked the answer and 16 subsets (including the set itself and null set) can be made from Set A. But in case there's a bigger set on a test. For example : A = (1,2,3,4,5,6) then I need a way to confirm whether my answer is right. So, IS THERE ANY FORMULA that can tell you the number of all possible subsets of a set??? (Provided it's like numbers or something. NOT - Solar system, and the subset of solar system is Earth. That's obviously common sense. My question is only regarding numbers or alphabets like, A = (a, b, c, d, e) or something.) Plz answer. Even if u don't know any such formula, answer by saying that there is no such formula. But if u read this question, PLEASE PLEASE answer! PLEASE PLEASE PLEASE PLEASE> Is there any such formula? If there is, what is the formula. Thank u.

  • Answer:

    I agree with Elizabeth, give her best answer! 16 possible subsets for a 4-element set. Element A can be in or out of any given subset. That's 2 ways. Element B can be in or out. That's another 2 ways. Element C can be in or out. 2 more ways. Element D can be in or out, again, 2 more ways. 2 x 2 x 2 x 2 = 16 and generalize to 2^n for n elements.

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If there are 5 elements in the Universal set, then a subset can contain each of the 5 elements, or not . The number of all possible subsets is therefore 2^5=32 and this includes the null set and the universal set. With 6 elements ??

Elizabeth M

Yes there is a formula. n(C)0+n(C)1+n(C)2+n(C)3+....+n(C)n But instead of learning the formula, let us try to develop it here. that way we will never forget it. Let us assume that each element in the given set is "ALWAYS DISTINCT". Let us start with a small set of two elements. its subset can have either of the two elements or both or none. Ex: subsets of {1,2} are (1), (2), null set and the set itelf. here just check how many sets of one element did we get - as many as there are elements in the given set i.e. 2 Therefore every set has so many subsets of ONE element as the number of DISTINCT ELEMENTS. Now let s take a bigger set {1,2,3} 3 sets of single element the given set null set AND So many sets of two elements each that can be made from the given superset. Now how many such sets can u make? n(C)2 Take a still bigger one {1,2,3,4} here comes n(C)3 and so on Therefore if u r given a set of 7 distinct elements answer is 7(C)0+7(C)1+7(C)2+7(C)3+7(C)4+7(C)5+7(C)… = 1+ 7+ 42 + 35 + 35 + 42 + 7 + 1 = 170

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