Exercise 10 Page 197

A set of numbers shown in roster form lists all elements belonging to the set. In set-builder notation, however, all of the elements in a set can be described using a logical statement.

Roster Form

We are given a few key pieces of information about this set of numbers: the numbers must be real numbers and factors of 12. For a number to be a factor, it must be a whole number that can be multiplied by another whole number to produce a number. 1* 12&=12 2* 6&=12 3* 4&=12 The numbers 1, 2, 3, 4, 6, and 12 can be multiplied in various combinations to produce 12. We can now write the roster form of set N. N={ 1, 2, 3, 4, 6, 12 }

Set-Builder Notation

This way of writing a set is often more compact. We can use some variable, such as x, to describe the elements of N and add a statement describing these elements. N={x|xis a real number that is a factor of 12}