Question

Use the roster method to represent the following sets:
i) The counting numbers which are multiples of 5 and less than 50.
ii) The set of all-natural numbers x which $x+6$ is greater than 10.
iii) The set of all integers x for which $30 / x$ is a natural number.

Answer 1

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets. An example of the roster method is to write the set of numbers from 1 to 10 as {1, 2, 3, 4, 5, 6, 7, 8, 9 and 10}. An example of the roster method is to write the seasons as {summer, fall, winter and spring}.

Complete step by step solution:
The two main methods for describing a set are roster and rule (or set-builder). A roster is a list of the elements in a set. When the set doesn't include many elements, then this description works fine.
(i) The counting numbers which are multiples of 5 and less than 50 are {5, 10, 15, 20, 25, 30, 35, 40, 45}
(ii) The set of all-natural numbers x which $\mathrm{x}+6$ is greater than 10.
$\mathrm{x}=\\{5,6,7,8, \ldots\\}$
(iii) The set of all integers $\mathrm{x}$ for which $\dfrac{30}{\mathrm{x}}$ is a natural number.
$\mathrm{x}=\\{1, 2, 3, 5, 6, 10, 15, 30\\}$

Note:
Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set. Set, in mathematics and logic, is any collection of objects (elements), which may be mathematical (e.g., numbers, functions) or not.