No. of subsets = 2n - 1
3 = 2n - 1
3 + 1 = 2n - 1 + 1
4 = 2n
4/2 = 2n/2
2/1 = 1n/1
2 = n
n = 2elements
The subsets of a fraction refer to the individual components that make up the fraction. For example, the subsets of the fraction 3/4 would be the numerator (3) and the denominator (4). In set theory, a subset is a set that contains elements of another set, so in the context of fractions, the subsets are the parts that form the fraction.
thenumber of subsets = 8formula: number of subsets =2n; wheren is thenumber of elements in the set= 2n= 23= 8The subsets of 1,2,3 are:{ }, {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3}
In a subset each element of the original may or may not appear - a choice of 2 for each element; thus for 3 elements there are 2 × 2 × 2 = 2³ = 8 possible subsets.
Well honey, the set {1, 2, 3, 4, 5, 6, 7, 8, 9} has 9 elements, so it will have 2^9 subsets, including the empty set and the set itself. That's a grand total of 512 subsets. Math can be sassy too, you know!
Well, honey, the number of subsets in a set with 9 elements is given by 2 to the power of 9, which equals 512. So, there are 512 subsets in the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Don't worry, I double-checked it just for you.
The subsets of the set {1, 2, 3, 4, 5, 6} include all possible combinations of its elements, including the empty set. There are a total of (2^6 = 64) subsets, which range from the empty set to the full set itself. Some examples of subsets are {1}, {2, 3}, {4, 5, 6}, and {1, 2, 3, 4, 5, 6}. Each subset can vary in size from 0 to 6 elements.
(5 x 4 x 3)/(3 x 2) = 10
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.
For example, if we have a set of numbers called A which has 3 members(in our case numbers): A={2,5,6} this set has 8 subsets (2^3) which are as follow: the empty set: ∅ {2},{5},{6} {2,5},{2,6},{5,6} {2,5,6}
Number of subsets with no members = 1Number of subsets with one member = 5.Number of subsets with 2 members = (5 x 4)/2 = 10.Number of subsets with 3 members = (5 x 4 x 3 /(3 x 2) = 10.Number of subsets with 4 members = (5 x 4 x 3 x 2)/(4 x 3 x 2) = 5.Number of subsets with 5 members = 1Total subsets = 1 + 5 + 10 + 10 + 5 + 1= 32.A set with n elements has 2n subsets. In this case n = 5 and 25 = 32.The proof in the case that n = 5 uses a basic counting technique which say that if you have five things to do, multiply together the number of ways to do each step to get the total number of ways all 5 steps can be completed.In this case you want to make a subset of {1,2,3,4,5} and the five steps consist of deciding for each of the 5 numbers whether or not to put it in the subset. At each step you have two choices: put it in or leave it out.
A finite set is a set with a finite number of elements. An infinite set has an infinite number of elements. Intuitively, if you count the elements in a finite set, you will eventually finish counting; with an infinite set, you'll never finish counting. One characteristic of infinite sets is that they can be placed in one-to-one correspondence with proper subsets of the set. For example, if A = {1, 2, 3, 4, ...} (the counting numbers), and B = {2, 3, 4, 5, ...} (the counting numbers, starting at 2), then B is a proper subset of A, and they can be placed in one-to-one correspondence like this: 1 <---> 2; 2 <---> 3; 3 <---> 4, etc. This means that, in a certain sense, the set and its proper subset have "the same number of elements". Such a one-to-one correspondence (between a set and one of its proper subsets) is not possible with finite sets.
If your 7 element set is {a, b, c, d, e, f, g}, you would list a 3 element subset by taking any 3 elements of the set eg., {a, d, g} or {b, c, f}, etc. To count all of the subsets, the formula is 7C3, where 7C3 is 7!/(3!*4!), or 35 different unique 3 element subsets of a 7 element set.