 A set, informally, is a collection of things considered to be a single object. Set notation requires the use of curly brackets, and the objects within these brackets are called the elements of the set. The elements in a set do not need to be in any order, but we will typically see numerical values in an order. Sets are usually named with a capital letter. Some sets have their own defined letter, and others are made up. For example, z is the set of integers or whole numbers. We can define our sets with our own letters, for example, e, for the set of even numbers. It also works for words, such as a, the set for animals. We also have something called the universal set. This includes everything we are looking for, and usually has the symbol epsilon. For example, with the letters of the English alphabet, v is the set for vowels, but included in the universal set are all letters. When we have two sets, we can look at how they are linked. We use this symbol, called intersection, to say something is in both sets we are looking at. We can use this symbol, union, to say that an object is in one set or the other. To say an object is not in a set, we use an apostrophe, like this. Let's see an example. Look at sets A and B. To find the set A into section B, we are looking for values which appear in both. Pause the video and see if you can identify it. The shared values are 10 and 20, so A into section B would look like this. For A union B, we are looking for values in either. Pause and try for yourself. The values 10 and 20 appear in each set, but only need to appear once in the union set, so A union B should look like this. Event diagrams are a useful way of looking at union and intersection, particularly for finding probabilities. If you see P, A, this is asking you for the probability an object is in set A. On a Venn diagram, P, A would look like this. For not in set A or P, A apostrophe, it would look like this, the inverse. Union where we share values on a Venn diagram is the central section. The probability of an object being in this section would be given the notation P, A, intersection B. Union the set A or set B notation looks like this on a Venn diagram. It has a larger area to choose from, because it only requires one or the other, not both. Typically, union probabilities are higher than intersection. The probability notation for this is given by P, A, union, B. Overall, there are eight variations of combination. If you can remember four, the other four are the opposites for A, B, and the link symbol. For example, this is P, A, intersection B. Notice the shaded shared section. The inverse area within the universal set has the opposite notation. So A and B gain apostrophes and intersection becomes union. P, A, apostrophe, union, B, apostrophe. This is the Venn diagram for P, A, union, B. Its inverse is given by notation P, A, apostrophe, intersection, B, apostrophe. Remember to find the opposite notation and change each symbol for its opposite. This is P, A, intersection, B, apostrophe. Can you work out the notation for the inverse Venn diagram? How did you do? P, A, apostrophe, union, B. Finally, P, A, apostrophe, intersection, B. Try and find the inverse notation. How did you get on? P, A, union, B, apostrophe. So there you have a quick guide to set notation. Applying union and intersection to Venn diagrams can be tricky. So taking them step by step is always advisable. If you liked the video, give it a thumbs up. And don't forget to subscribe. Comment below if you have any questions. Why not check out our Fusco app as well? Until next time.