Use the Venn diagram below to find
the intersection of 𝑋 ∪ 𝑌 and 𝑍.
This symbol means union. It means the elements in either or
both sets. This symbol means intersection. It is the elements found in both
sets. So let’s first take a look at our
Venn diagram. The elements of 𝑌 are three, nine,
six, and five. The elements of 𝑋 are six, five,
one, seven, and four. The elements of 𝑍 are seven and
So let’s begin with finding the
union of 𝑋 and 𝑌. So we want the elements that are in
either 𝑋 or 𝑌 or in both sets. Three is in set 𝑌. Nine is in set 𝑌. Six is in both 𝑋 and 𝑌. Five is in both 𝑋 and 𝑌. One is in 𝑋. Seven is in 𝑋. And four is in 𝑋.
Now we want to take 𝑋 union 𝑌 and
intersect it with 𝑍. So we want to take these elements
and intersect them with the elements of 𝑍, seven and four. And the intersection are the
elements found in both sets. So what number or numbers is found
in both of these sets? Seven and four.
So once again our answer is the
elements seven and four.