Do The Following Exercises. 4. Answer This Question: How Many Subsets Does A Set Of N Elements Have?
Do the following exercises. 4. Answer this question: How many subsets does a set of n elements have?
Answer:
The answer is 2^n.
Step-by-step explanation:
Let us define first what is a subset.
A subset is a set that can be found in a given set.
Examples:
A={5}
The subsets are: {5} and { }. There are 2 subsets in the given set that has only 1 element.
B = {2,4}
The subsets are: {2}, {4}, {2,4}, { }. There are 4 subsets in the given set that has 2 elements.
C = {1,3,5}
The subsets are: {1}, {3}, {5}, {1,3}, {1,5}, {3,5}, {1,3,5}, { }. There are 8 subsets in the given set that has 3 elements.
Looking at the pattern,
1 element = 2 subsets
2 elements = 4 subsets
3 elements = 8 subsets
We can derive a formula in finding the number of subsets.
That is, the number of subsets given n as the number of elements is 2^n.
2^1 = 2
2^2 = 4
2^3 = 8
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