identify n(S) for the given set:

S={5,10,15,20,25,30,...}

To identify n(S) for the given set S, we need to find the number of elements in the set.

Here, the set S consists of numbers that are multiples of 5 starting from 5. The pattern is clear: 5, 10, 15, 20, 25, and so on.

We can observe that each element in the set can be written as 5n, where n is a positive integer greater than or equal to 1. Since we are looking for the number of elements in the set, we need to find the range of values for n.

If we divide any number in the set by 5, we get n. For example, 5 divided by 5 is 1, 10 divided by 5 is 2, 15 divided by 5 is 3, and so on. Notice that n takes values from 1, 2, 3, and onwards.

Since n represents the number of elements in the set S, we can conclude that:

n(S) = Set of positive integers starting from 1.

Therefore, n(S) is the set of all positive integers.