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Today we're going to explore mathematical sets, which are surprisingly simple! Sets are just collections of any objects or concepts, also known as elements, that can be related to each other through union or intersection.
A set is a collection of objects, and it doesn't need to be a number!
This is the set of the clothes in my closet: C = {pants, t-shirt, skirt and dress}. The capital C represents the set. So, if I said set C, we know I'm talking about clothes in my closet. The braces, { }, denote the elements, or members of the set. The elements of set C are pants, t-shirt, skirt and dress.
You're probably familiar with a set of real numbers: R = {?-3, -2, -1, 0, 1, 2, 3...}. The three dots indicate that the pattern continues. The elements of this group are all real numbers. So, R equals the set of real numbers.
To collect sets together, we use the term union. We unite the sets into one.
Let's say I have two sets. Set A is green, blue and pink. Set B is orange, yellow and black. A u B represents the union of sets A and B. Yes, that u symbol represents union! It's kind of handy! A u B represents all the elements that are listed in set A or in set B or in both. How would that look in using mathematical symbols? A u B = {green, blue, pink, orange, yellow, black}.
To find elements in common with sets, we use the term intersection. Think of the sets as two roads that meet at an intersection. What do the two roads, or sets, have in common?
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Let's say I have two sets. Set A is 4, 6 and 9. Set B is 7, 8 and 9. A intersect B represents the intersection of sets A and B. Yes, that upside down u represents intersection! This represents all the elements that are the same in A and B. How would that look in using mathematical symbols? A intersect B = {9}.
Let's review what we just talked about. A set is a bunch of objects. It could be numbers, letters, anything. To show a set, we always use a capital letter. To show the numbers, or the elements, of a set, they always go between theses braces, { }, or these curly-q parentheses. Union is when we unite things - when we're going to put things together. So, A u B means that we're going to put everything in A together with everything in B. Remember, intersection is where things are the same - where they intersect at. So, if I say A intersect B, what I'm looking for is any element, or number, that are common in A and B.
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