We're going to continuing working with inequalities but before we, do let's look at sets. >> Sets are going to help us understand the words and, and or. >> And then, we can use these words to make sense of compound inequalities next. >> C is going to be the set of the counting numbers from 1 to 7. >> A set is a collection of elements or items ... >> And it's usually denoted by curly braces on both ends. >> For the first question of this section, what's the set of even numbers between 1 and 9? >> You can enter your answer here. >> Be sure you use the correct punctuation notation. >> Commas separate the elements.
Even numbers are divisible by 2. >> So, I know I need to include any numbers between 1 and 9 that can be divided by 2. >> So, I have 2, 4, 6, and 8. >> To find the set of even numbers between 1 and 9, we just list them off, 2, 4, 6, 8. We use curly braces on both ends and commas between the elements. >> Nice work.
Here I have my set of counting numbers from 1 to 7 and my even numbers between 1 and 9. We're going to write these sets inside of circles so you can better visualize them. Here I have my set C of numbers, and here I have my set E of numbers. I've drawn my two sets in overlapping circles, or a Venn Diagram. All the elements of C have been placed inside this circle and all the elements of E have been placed inside this circle. What's neat about each of these sets is we can actually make one giant set, called the union. To find the union, we want any element that's in set C or in set E, in any of the circles. The union is represented by this upward U symbol, so what set do you think is C union E? Enter your answer here.
To find the set of C Union E, you want any elements that are in set C or in set E. So, I list the numbers, usually in order, with curly braces on the ends and with commas in between. For the 2, 4, and 6, I don't need to list them twice. I know that they're in set C and in set E, but I only need to list them once in the Union.
When looking at the union, we can also notice that 8 is an element of E but not an element of C. When we're trying to find the union, we list any element that is in one of the sets or the other. So, 8 would be in our union. We also have this other word called intersection. The intersection is a little bit easier. It's all the elements that are in set C and in set E. We use this upside-down u to denote intersection.
So, let's see if you can get this one. >> What is the intersection of c and e? Enter your set in this box here.
If you said 2, 4, and 6, nice work. >> We know 2, 4, and 6 are both elements of C and E. And we can also see that in our Venn Diagram. >> We just wanted the center numbers or the numbers that are elements that were in both set C and set E.
When working with sets, we don't always have to work with numbers. We can also have letters. So here I have set m, and it contains the letters of math. And set y which contains the letters of udacity. For this quiz, I want you to find the intersection of m and y, and the union of m and y. You want to put your answers here. You'll need to remember what each symbol means. I've drawn a venn diagram to help you out. This is always a great way to get started. Good luck.
Let's answer this quiz by filling in our Venn diagram. I'm going to put the letters of M in this circle and we'll put the letters of Y in this circle. I should 1st look at M and Y to see which letters overlap between the sets. I know the letters a and t are in both of the sets, so I'm going to list those in, In the middle. We can remember that the letters in the middle are the inner section. It's what shared, or what's between m and y. So for the intersection of m and y, we have the set a and t. The other letters are just listed in their respective sets, And then for the union, we want to list everything once. So we have this set, the letters of m or the letters of y, the union.
For this problem, I have two sets, A and B. I have A equals 1,5,9,15, and 17. And set B contains the elements 2,5,8,12,15, and 18. Can you find A intersection B, and A union B? You can put your answers in these boxes. I've already put the curly brackets for you, so when you enter your answer, just separate the elements with commas.
The intersection of A and B contain the elements 5 and 15. The union of A and B contain the elements 1, 2, 5, 8, 9, 12, 15, 17 and 18. How do we get that the intersection of A and B just contains 5 and 15? We know that intersection means and. So, we have to find the numbers that are in set A and in set B. Well, there's only two numbers that are in both sets. Here, 5 is in both sets, and 15 is in both sets. And those are the only two numbers that are in both sets. So, the intersection of A and B is 5 and 15. When I want to find the union of two sets, I know that union means or. So, I want all of the elements that are in set A or in set B, which basically means all of the elements in both sets. So, I have 1, 2, 5. Now, even though five is in both sets, we only write it one time. And then I have 8, 9, 12, and again 15 is in both sets, but we only write it once. And then I have 17, and I have 18.