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

If ๐‘‹ = {8, 6, 2} and ๐‘Œ = {7, 3, 9}, which Venn diagram represents the two sets?


Video Transcript

If ๐‘‹ is the set of elements eight, six, and two and ๐‘Œ is the set of elements seven, three, and nine, which Venn diagram represents the two sets?

Letโ€™s begin by going through each option and seeing what they entail. For option a, we have the ๐‘‹ elements, the ๐‘Œ elements, and this portion is the ๐‘‹ and ๐‘Œ elements, so the elements that are in both. Itโ€™s called the intersection of the sets.

For option b, ๐‘‹ is the entire box. So any number that is in this box is in the set. And then ๐‘Œ 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 ๐‘Œ must be in ๐‘‹. So ๐‘Œ would be a subset of ๐‘‹.

For option c, ๐‘‹ and ๐‘Œ are represented by the entire circle. Which means they share all of the exact same elements.

And then for option d, set ๐‘‹ and set ๐‘Œ are totally separate and they donโ€™t overlap. Meaning, they donโ€™t have any elements in common.

So letโ€™s begin by looking at set ๐‘‹ and ๐‘Œ and determine which one a, b, c, or d would be the best Venn diagram to represent the two sets. So ๐‘‹ holds the elements eight, six, and two. ๐‘Œ 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 donโ€™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 donโ€™t. Two is in the set ๐‘‹ and seven is in the set ๐‘Œ. But itโ€™s not in both. So if we know that they donโ€™t have any elements in common, this can actually go pretty quickly. Because option b is saying that all of the elements in ๐‘Œ are actually also in ๐‘‹. And thatโ€™s not the case. None of ๐‘Œโ€™s elements are actually in ๐‘‹.

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, ๐‘‹ and ๐‘Œ each only have three elements.

So this leaves us with option d. It says that set ๐‘‹ should have elements two, which it does, six, and eight. And thatโ€™s great for ๐‘‹. And then ๐‘Œ should have nine, seven, and three. And none of these are the same. So they shouldnโ€™t overlap. So this means the best Venn diagram to represent the two sets would be option d.

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