Describe the following set by property method:
{3,5,9,17,33}
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{3, 5, 9, 17, 33} can be written in set builder form as: {2^n + 1: nϵN, 1≤n≤5}
Step-by-step explanation:
In mathematics, a set is a well-defined collection of objects.
Example: ‘The rivers of India’ is a well-defined collection. From the property we know that Ganga belongs to the set while Nile does not belong to the set.
The property is the common rule that binds all the elements of the set. In this example, the property of the set is that all the elements are within India.
The set {3, 5, 9, 17, 33} can be written in set builder form as:
{2^n + 1: nϵN, 1≤n≤5}
2^1 + 1 = 2 + 1 = 3
2^2 + 1 = 2 + 2 = 5
2^3 + 1 = 8 + 1 = 9
2^4 + 1 = 16 + 1 = 17
2^5 + 1 = 32 + 1 = 33
We get all the elements of the set for values of n from 1 to 5.
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