Find the set of elements common to 𝑋, 𝑌, and 𝑍.
So we want to know what elements do these sets have in common. Let’s begin by listing all of the elements in each set. 𝑋 includes elements four, one, eight, five, seven, and six. Set 𝑌 includes elements six, five, seven, three, and two. Lastly, set 𝑍 includes elements nine, eight, five, seven, and three.
So looking at our Venn diagram, where is it that all three of these circles overlap? That will be here in the green. So the elements common to sets 𝑋, 𝑌, and 𝑍 should be five and seven.
Let’s go ahead and check our lists. All of the sets include five. And all of the sets include seven. Are there any other elements that are found in all three sets? No, there’s not. Therefore, the set of elements common to 𝑋, 𝑌, and 𝑍 would be five and seven.