# Question Video: Using Venn Diagrams to Represent Two given Sets Mathematics • 10th Grade

If π = {8, 6, 2} and π = {7, 3, 9}, which Venn diagram represents the two sets?

02:48

### Video Transcript

If π is the set of elements eight, six, and two and π is the set of elements seven, three, and nine, which Venn diagram represents the two sets?

Letβs begin by going through each option and seeing what they entail. For option a, we have the π elements, the π elements, and this portion is the π and π elements, so the elements that are in both. Itβs called the intersection of the sets.

For option b, π is the entire box. So any number that is in this box is in the set. And then π 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 π must be in π. So π would be a subset of π.

For option c, π and π are represented by the entire circle. Which means they share all of the exact same elements.

And then for option d, set π and set π are totally separate and they donβt overlap. Meaning, they donβt have any elements in common.

So letβs begin by looking at set π and π and determine which one a, b, c, or d would be the best Venn diagram to represent the two sets. So π holds the elements eight, six, and two. π 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 donβ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 donβt. Two is in the set π and seven is in the set π. But itβs not in both. So if we know that they donβt have any elements in common, this can actually go pretty quickly. Because option b is saying that all of the elements in π are actually also in π. And thatβs not the case. None of πβs elements are actually in π.

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, π and π each only have three elements.

So this leaves us with option d. It says that set π should have elements two, which it does, six, and eight. And thatβs great for π. And then π should have nine, seven, and three. And none of these are the same. So they shouldnβt overlap. So this means the best Venn diagram to represent the two sets would be option d.