Question Video: Identifying the Difference between Two Known Sets | Nagwa Question Video: Identifying the Difference between Two Known Sets | Nagwa

Question Video: Identifying the Difference between Two Known Sets

What is ๐‘‹ โˆ’ โˆ…?


Video Transcript

What is set ๐‘‹ subtract a โˆ… 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 weโ€™re 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 โˆ… set. Remember that a โˆ… set is an empty set. This is a set that doesnโ€™t contain any elements at all.

Now, we donโ€™t know whatโ€™s in set ๐‘‹. But this doesnโ€™t matter. We can invent an example. And it will still help us to answer the question. Weโ€™ll call this circle set ๐‘‹. And weโ€™re going to have to put some elements in it. There must be elements in there. Otherwise, it would be a โˆ… set and it would be labelled as a โˆ… set. It doesnโ€™t matter what elements we use. But we do need some for our example. So letโ€™s 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 โˆ… set. Hereโ€™s our โˆ… set. Itโ€™s got no elements in it at all. So what happens if we subtract this โˆ… set from set ๐‘‹? What are we left with? Weโ€™re left with all the elements of set ๐‘‹, just as they were. Subtracting an empty set from set ๐‘‹ hasnโ€™t 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 โˆ… 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 โˆ… set leaves us with set ๐‘‹.

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