Will Form 8865 Exclusion 2023-2024

Okay, this video is going to be about what's known as the principle of inclusion exclusion. What this is, is a counting technique. Ultimately, the goal is to derive a formula that will help us find the number of elements in the union of any sets, whether those sets are disjoint or not. This is going to be part one of at least a few parts. In this example, we'll talk about situations where we only have two or three sets, and that will allow us to spot a bit of a pattern. In the next part, we will introduce more notation and make everything more precise. We will derive the formula and prove it, and then we will do more examples to get a better understanding of how to solve these types of problems. Let's start with a basic example. Suppose we have a group of students who are studying logic or mathematics. If we ask them, we find that twelve of them are studying logic, twenty-six are studying mathematics, and five are studying both subjects. One thing to be careful about is that if 12 of them are studying logic, it doesn't mean they are only studying logic. The same goes for the 26 students studying mathematics. We want to know how many students are in the group. To set this up, we can use a Venn diagram. Let A be the group of students studying logic and B be the group of students studying mathematics. We want to find the number of students in the group of A or B. The little Union symbol stands for "or". The bars represent the number of elements in each set. Let's make a Venn diagram. Set A represents the people studying logic, and set B represents the people studying mathematics. There is some...