### Video Transcript

What is set ๐ subtract a โ
set?

Instead of numbers, there are two symbols in this subtraction. And it might be worth starting off by thinking about what these two symbols might mean. Firstly, we have the letter ๐, a capital ๐. Often in math, the letter ๐ will represent a number and it will have a value. But as weโre going to go in to see this question is about sets. And so, we can take this letter ๐ to mean set ๐. In other words, a set of different elements and we call the whole group ๐. Our second symbol is the one that we used to represent a โ
set. Remember that a โ
set is an empty set. This is a set that doesnโt contain any elements at all.

Now, we donโt know whatโs in set ๐. But this doesnโt matter. We can invent an example. And it will still help us to answer the question. Weโll call this circle set ๐. And weโre going to have to put some elements in it. There must be elements in there. Otherwise, it would be a โ
set and it would be labelled as a โ
set. It doesnโt matter what elements we use. But we do need some for our example. So letโs imagine this is a set of house numbers of children in a class. Some do live at number 23, 87, and number 12, perhaps number 35 as well.

Now, from this set, we need to subtract a โ
set. Hereโs our โ
set. Itโs got no elements in it at all. So what happens if we subtract this โ
set from set ๐? What are we left with? Weโre left with all the elements of set ๐, just as they were. Subtracting an empty set from set ๐ hasnโt changed it in the slightest. It still contains all the elements it had to begin with.

So in a way, we can say that subtracting a โ
set from a set is a little bit like subtracting zero from a number. The set stays the same. And so, set ๐ subtract a โ
set leaves us with set ๐.