Video: Finding the Difference of Two Sets Using Venn Diagrams

Video Transcript

Using the Venn diagram, find not 𝑌 minus 𝑋.

So, what we are going to look at first is the notation used. And we can see that we have “find” and then we’ve got 𝑌 prime minus 𝑋. And what this mean is “find” and then, because of the prime that’s with the 𝑌, it is the complement of set 𝑌. What does that mean? Well, complement of set 𝑌 is the elements not in set 𝑌. And then, we subtract the elements that are in set 𝑋.

So, first of all, what we’re going to do is we’re gonna identify what is the complement of set 𝑌 so, i.e., the elements that are not in set 𝑌. So, the elements that are not in set 𝑌, we’ve got seven, three, six, eight, and two. And the reason they’re not in set 𝑌 is because if we have a look at the right-hand side of our Venn diagram, we got an oval. And within that oval, we have one and nine, which are elements only in set 𝑌, and five and four, which are elements that are both in set 𝑌 and set 𝑋. So therefore, the only ones that are not in set 𝑌 are seven, three, six, eight, two as we already said.

So, as we said, that’s our not 𝑌. So, now, what we’re gonna have look at is the elements that are in set 𝑋. Well, I’ve circled these in green. And these are seven, three, five, and four. And we include five and four because they’re both in set 𝑋 and set 𝑌.

So therefore, if we put this together, what we’ve got is the elements that are not in set 𝑌, which is seven, three, six, eight, two. And then, we’re gonna take from them the elements that are in set 𝑋, which is seven, three, five, and four. Well, first of all, we can take the number seven away, cause this is an element in both, and then the number three, cause again this is an element in both. And we’re subtracting any element that’s in set 𝑋 away from any element that is not in set 𝑌.

Well, the element which is the number five, this isn’t in not set 𝑌. So therefore, this won’t change it. As is the same with number four because this is not in the set not 𝑌. So therefore, the elements we’re left with are six, eight, and two. So therefore, we can say that using the Venn diagram, we found that not set 𝑌 minus set 𝑋 leaves us with the elements six, eight, and two.