Relative complement or difference between sets | Probability and Statistics | Khan Academy

TL;DR

Sets can be subtracted from each other to find the elements that are unique to each set and the relative complement between them.

Transcript

What we're now going to think about is finding the differences between sets. And the first way that we will denote this is we'll start with set A. I've already defined set A. Let me do it in that same shade of green. I've already defined set A here. And in both cases, I've defined these sets with numbers. Instead of having numbers as being the obje... Read More

Key Insights

• 😫 Sets can be subtracted from each other to find the unique elements.
• 😫 The difference between sets can be represented by subtracting one set from another.
• 😫 The relative complement of one set in another represents the elements that are not in the second set but are in the first set.
• 😫 Subtracting an element from a set that doesn't contain it doesn't change the set.

Questions & Answers

Q: How do you find the difference between sets?

To find the difference between sets, subtract the elements of one set from the other. This will give you the elements that are unique to each set.

Q: What does the relative complement of set B in set A represent?

The relative complement of set B in set A refers to the elements that are not in set B but are in set A. It can also be seen as the elements of set A minus the elements of set B.

Q: What happens when you subtract an element from a set that doesn't contain it?

If you subtract an element from a set that doesn't contain it, it doesn't affect the set. The resulting set will remain unchanged.

Q: What is the relative complement of set A in set A?

The relative complement of set A in set A is the empty set, also known as the null set. This means that there are no elements in set A that are not also in set A.

Summary & Key Takeaways

• Sets can be represented by numbers or other objects and can be subtracted from each other to find the elements unique to each set.

• Subtracting set B from set A gives the elements that are in set A but not in set B.

• The relative complement of set B in set A refers to the elements that are not in set B but are in set A.