The union of

X

and

Y

contains all elements that are in

X

and

Y .

Notice that we do not count an element twice if it exists in both sets. First, we need to rewrite

X

as a set of all integers that are odd and less than 16.

X X = {x ∣ x is an odd whole number less than 16} = {1, 3, 5, 7, 9, 11, 13, 15}

Now we can find the union of those two sets.

X Y X \cup Y = {1, 3, 5, 7, 9, 11, 13, 15} = {2, 6, 9, 10, 16} = {1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 15, 16}

Knowing

X \cup Y,

we can find the union of

X \cup Y

and

Z .

This will give us

X \cup Y \cup Z .

To do this, we start by rewriting

Z

as a set of all integers that are even and less than

19 .

Z Z = {x ∣ x is an even whole number less than 19} = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18}

The union of

X \cup Y

and

Z

contains all elements that are in

X \cup Y

and

Z .

Again, we do not count an element twice if it exists in both sets.

Z X \cup Y X \cup Y \cup Z = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18} = {1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 15, 16} = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18} .

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