Chapter 3.5, Problem 46PPE

To determine

To find: The set of elements which are not part of the universal set

Answer to Problem 46PPE

The set C’ is given as, $\text{C' = {2, 6, 10, 14}}$ .

Explanation of Solution

Given:

A universal set where the elements are multiple of 2 and less than 18 and $\text{C = {4, 8, 12, 16}}$ .

Calculation:

Universal set is a set of elements which contains all the numbers or variables for the given condition.

A set of elements which contains few elements of universal set is the subset of that universal set while the complement of that set is the set which contains elements of universal set other than that subset.

Let U = Universals set

C = Subset of universal set

C’ = Complement set

In the universal set it is mentioned that the elements are multiple of 2 and less than 18.

Thus,

  $\text{U}\text{=}\text{{2,}\text{4,}\text{6,}\text{8,}\text{10,}\text{12,}\text{14,}\text{16}}$

Given,

  $\text{C = {4, 8, 12, 16}}$

Thus,

  $\text{C' = {2, 6, 10, 14}}$