Use the symbol for is a subset of or is not a subset of to fill in the gap. The Venn diagram shows a set containing the elements five and one what the intersection between 𝑋 and 𝑌.
Perhaps the most common Venn diagram that we use in maths is one where we use two, maybe three, circles. Well, the diagram in this question is still a Venn diagram, but there are no circles. It’s made up of a blue oval shape and an orange square. But they’re both ways of showing sets of numbers. And it’s still a Venn diagram. Before we go through the question, let’s spend a few moments looking at the diagram and trying to understand it. So we can see that we have two sets of numbers 𝑋, which is the blue oval shape, and 𝑌, which is the orange square shape. And we know that everything within the oval is in set 𝑋. So that’s the numbers two, eight, one, six, and nine.
Similarly, everything within the orange square shape is in set 𝑌. That’s the numbers four, five, three, six, and nine. What did you notice as we read those numbers together? Both sets have some numbers in common. And this is the overlap or the intersection between both shapes. On this particular Venn diagram, we can see that the intersection is the part that’s colored both blue and orange. The numbers six and nine are in the oval shape. They’re also in the square. Now, this intersection between 𝑋 and 𝑌 is mentioned in the question. Can you see? It’s this expression here. This symbol that looks a little bit like a bridge shape represents the intersection between two sets.
And in this statement, we can see 𝑋 and 𝑌 either side of it. So it’s talking about the intersection between set 𝑋 and set 𝑌. In other words, it’s talking about the overlapping part we were just discussing. The part with the numbers six and nine in it. Now, there are two more symbols in this question that it might make sense to just quickly go over. These are the symbols that we need to choose from to fill in the gap. The first symbol represents is a subset of, and the second symbol represents is not a subset of. We know that when something is a subset of something else, it’s contained within it. So in the question, we’re given two expressions to do with the Venn diagram. So the question then goes on to give us a sentence about the Venn diagram.
We’re told that the Venn diagram shows us something. But what does it show us? The two expressions that we’re given are a set involving the numbers five and one and also that intersection between 𝑋 and 𝑌 that we talked about. Now, either a set that involves the numbers five and one is a subset of the intersection between 𝑋 and 𝑌 or is not a subset of the intersection between 𝑋 and 𝑌. Which of these symbols should we use? Remember that if something is a subset of something else, it’s contained within it.
So what’s contained within the intersection between 𝑋 and 𝑌? We can see the number six. We can see the number nine. And We can see them both together. The numbers six and nine. All of these are subsets of the intersection between the two parts of the Venn diagram. But look at where the numbers five and one are. Five is over here. It’s Just in 𝑌; it’s not in 𝑋 at all. And the number one is over here. It’s in 𝑋, but it is not in 𝑌 at all. So we can say that a set that contains five and one is not a subset of the intersection between 𝑋 and 𝑌. The correct symbol to use is this one. The Venn diagram shows that a set containing the elements five and one is not a subset of the intersection between 𝑋 and 𝑌.