Write the following sets using roster method and set builder notation.

Question

A.     Write the following sets using roster method and set builder notation.

a.        Set of all factors of 15

b.       Set of all solution of the equation 8x=0

c.        Set of all integer’s solution of 2x^2 = 8

Answer 1

The roster method of a set is very simple: it's just a list of the elements of the set enclosed by curly brackets. Set-builder notation is a bit more powerful as it describes the elements of the set rather than listing them so you can construct sets with large or even infinite cardinalities easily. For my answer, I'll write the roster method first and then the set-builder method.

a. S = {-15, -5, -3, -1, 1, 3, 5, 15} = {x ∈ Z | 15/x ∈ Z}

In the set-builder notation, I am building a set of all integer x such that 15/x is an integer, meaning x is a factor of 15.

b. S = {0} = {x ∈ R | 8x = 0}

c. S = {-2, 2} = {x ∈ Z | 2x^2 = 8}

These are not the only ways to define these sets, but they should work for the purposes of your question.