If 𝑋 is the set of elements eight, six, and two and 𝑌 is the set of elements seven, three, and nine, which Venn diagram represents the two sets?
Let’s begin by going through each option and seeing what they entail. For option a, we have the 𝑋 elements, the 𝑌 elements, and this portion is the 𝑋 and 𝑌 elements, so the elements that are in both. It’s called the intersection of the sets.
For option b, 𝑋 is the entire box. So any number that is in this box is in the set. And then 𝑌 are all of the elements inside of the circle. But notice the circle is inside of the box. Which means all of the elements of 𝑌 must be in 𝑋. So 𝑌 would be a subset of 𝑋.
For option c, 𝑋 and 𝑌 are represented by the entire circle. Which means they share all of the exact same elements.
And then for option d, set 𝑋 and set 𝑌 are totally separate and they don’t overlap. Meaning, they don’t have any elements in common.
So let’s begin by looking at set 𝑋 and 𝑌 and determine which one a, b, c, or d would be the best Venn diagram to represent the two sets. So 𝑋 holds the elements eight, six, and two. 𝑌 holds the elements of seven, three, and nine. So right away, what is their intersection? What do they have in common? Do they have any elements in common? They don’t. So their intersection would be the empty set.
So that means we can eliminate option a because it says that they share elements two and seven. And they don’t. Two is in the set 𝑋 and seven is in the set 𝑌. But it’s not in both. So if we know that they don’t have any elements in common, this can actually go pretty quickly. Because option b is saying that all of the elements in 𝑌 are actually also in 𝑋. And that’s not the case. None of 𝑌’s elements are actually in 𝑋.
And then for option c, it says that they have the exact same elements, that they all have elements eight, two, seven, three, six, and nine. And actually, 𝑋 and 𝑌 each only have three elements.
So this leaves us with option d. It says that set 𝑋 should have elements two, which it does, six, and eight. And that’s great for 𝑋. And then 𝑌 should have nine, seven, and three. And none of these are the same. So they shouldn’t overlap. So this means the best Venn diagram to represent the two sets would be option d.