how many subsets in all are there of a set containing 3 elements
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to find out the no. of subsets
the power of 2 is raised equal to the no. of elements in the set .
here no. of elements is 3 then the ans. is 8
the power of 2 is raised equal to the no. of elements in the set .
here no. of elements is 3 then the ans. is 8
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Given a set {1,2,...,n}{1,2,...,n}, how would one go about finding the number of subsets that contain the number 2, for example.
Having had a play around with this myself I've got as far as realising that the number of sets that contain the number nn is 2n−12n−1, but this was only through listing out the power sets of a few sets and seeing how many subsets contained the last element of the set. A messy and very unreliable method, I'm sure you'll agree.
Say if I had the set {1,2,3,4,5}{1,2,3,4,5} and I wanted to know how many subsets within the power set contained the element 3, would I have to list out the entire power set and risk making a fatal mistake or is there some sort of a formula that will provide me with an answer?
Having had a play around with this myself I've got as far as realising that the number of sets that contain the number nn is 2n−12n−1, but this was only through listing out the power sets of a few sets and seeing how many subsets contained the last element of the set. A messy and very unreliable method, I'm sure you'll agree.
Say if I had the set {1,2,3,4,5}{1,2,3,4,5} and I wanted to know how many subsets within the power set contained the element 3, would I have to list out the entire power set and risk making a fatal mistake or is there some sort of a formula that will provide me with an answer?
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