Sets X, Y, and Z are shown below. What is the average (arithmetic mean) of the elements of set Z?X = {1,2,3,4} Y = {2,4,6,8} Z = X ∪ Y...

To determine the arithmetic mean of the elements of the
set Z, we'll have to determine what are the elements of
Z.

We notice that the set Z is the result of union of the
sets X and Y. We'll recall that the resulting set Z consists of all distinct elements of
X and Y.

We notice that all distinct elements of Z are: Z =
{1,2,3,4,6,8}.

Now, we'll recall the definition of the
arithmetic mean: the sum of all elements divided by the number of
elements.

In this case, the sum of distinct elements is:
1+2+3+4+6+8 = 24

The number of elements of Z is
6.

a.m. = (1+2+3+4+6+8)/6

a.m.
= 24/6

a.m. =
4

We notice that the arithmetic mean is a.m.
= 4, therefore the right option is d.4.