GRE General

Sub Topics

Mathematical Sets Elements Intersections Unions Cardinality Types of Subsets (Infinite Finite Equal Empty)Categorical Propositions Subject Predicate Equivalent Infinite Sets What is a Two-Way Table

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GRE General: Venn Diagrams Subset Disjoint Overlap Intersection Union
Mathematical Sets Elements Intersections Unions

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.

Mathematical Sets Elements Intersections Unions

Understanding Sets

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.

Unions

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}.

Intersections

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? 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}.

Lesson Summary

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 members, or the elements, of a set, they always go between braces, { }, or these curlicue 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 elements, or members, that are common in A and B.

Learning Outcome

After watching this lesson, you should be able to identify concepts of sets, such as elements, and how they're related through union and intersection.