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Let S be a set which has N elements.
Consider in how many ways we can choose a subset.
List the N elements of the set S.
Let the names of the N elements be,
x1, x2, x3, . . . xN
For an arbitrary subset,
we have two choices for x1.
Namely, x1 might or might not be in the subset.
We have two choices for x2.
Namely, x2 might or might not be in the subset.
We have two choices for x3.
Namely, x3 might or might not be in the subset.
. . .
We have two choices for xN.
Namely, xN might or might not be in the subset.
Now we can easily count the total number of ways to choose
a subset.
2 choices for x1 times 2 choices for x2 times . . .
= 2 to the Nth power choices of ways to choose a subset.
This proves that the number of subsets of a set with
N elements is 2 raised to the Nth power.
Kermit Rose
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What is an improper subset?
An improper subset is identical to the set of which it is a subset. For example: Set A: {1, 2, 3, 4, 5} Set B: {1, 2, 3, 4, 5} Set B is an improper subset of Set Aand vice versa.
How many subset can you form in algebra?
If you have a set with "n" elements, you can form 2 to the power n subsets. This is because each element of the original set has two options: to be included, or not to be included, in a subset. So, for instance, for a set with four elements, you have 2 x 2 x 2 x 2 different possibilities to create subsets (2 to the power 4).Note 1: This includes the empty set, and the original set itself. Note 2: The set of all subsets is known as the power set. Note 3: It has been proven that the power set (of size 2 to the power n) is ALWAYS larger than the original set (of size n) - even for infinite sets. That means that the power set of an infinite set gives you a larger kind of infinity.
How many subset does a set of 5 elements have?
2^5=32
What subset is?
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}
How many subsets does a set have if the set has four elements?
16 Recall that every set is a subset of itself, and the empty set is a subset of every set, so let {1, 2, 3, 4} be the original set. Its subsets are: {} {1} {2} {3} {4} {1, 2} {1, 3} {1, 4} {2, 3} {2, 4} {3, 4} {1, 2, 3} {1, 2, 4} {1, 3, 4} {2, 3, 4} {1, 2, 3, 4} * * * * * A simpler rationale: For any subset, each of the elements can either be in it or not. So, two choices per element. Therefore with 4 elements you have 2*2*2*2 or 24 choices and so 24 subsets.
