Note-Taking Guides. How to use these documents for success

Transcription

1 1 Note-Taking Guides How to use these documents for success Print all the pages for the module. Open the first lesson on the computer. Fill in the guide as you read. Do the practice problems on notebook paper (usually). Put the notes and practice problems in a notebook. You can use these anytime! Review the notes before you go to sleep. Short term memory is converted to long term memory ONLY while you sleep. Your brain starts at the end of your day and converts things to long term memory in reverse order.

2 2 Module # Venn Diagrams Part 1: Sets A set is Numbers or objects within a set are called A set that has no members is called an set and can be written as or. A subset of a larger set is. Part 2: Venn Diagrams A Venn Diagram is. The rectangle represents. The circles represent. Do the circles always overlap? Why or why not?. Venn Diagram Fill in the following diagram as the questions are answered in the lesson: Sophomore Students Now do the practice problems, check your work and seek help if necessary.

3 Union of Sets What results from the union of two sets? Union is identified by what symbol?. Circle the elements of Set A and Set B that will be part of A U B: When creating a set, in what order should elements be listed?. Set C =. How do we list duplicate numbers in the new union set? For example, consider the sets D = {all 4 legged animals} and E = {all 8 legged animals}. Find the new set F = D U E. Sometimes it is not practical to list all elements of a set, but we can still combine them. Our new set will contain all the elements from set D and all the elements from set E. Set F =. Be sure to do the practice problems and check your answers. Seek help if needed.

4 Intersection of Sets What results from the intersection of two sets? Intersection is identified by what symbol?. Circle the elements of Set A and Set B that will be part of A B: When creating a set, in what order should elements be listed?. Set C =. Consider the sets D = {all 4 legged animals} and E = {all 8 legged animals}. Find the new set F = D E. We know that the intersection of these two sets will be a new set that contains only. So, we need to ask ourselves, Are there any animals that have both 4 legs and 8 legs? Circle: Yes or No Set F =. Because the new set has no elements, it is called an.

5 5 Consider the sets P = {Florida residents who have lived in the State over 5 years} and Q = {Florida residents who have lived in the State less than 20 years.}. Find the new set S = P Q. We know that the intersection of these two sets will be a new set that contains only. So, we need to ask ourselves, Are there an Florida residents that have lived in the state more than 5 years and less than 20 years? Circle: Yes or No Set S =. Set S =. Finally Set S =. Now, do the practice problems and seek help if needed.

6 Complements of Sets Besides being perhaps the easiest concept in this module, the complement of a set is To find the complement of a set, we need to know the universal set, which is The symbol for the complement of Set A (in this course) is. Set A = {even numbers}. To find Ã, we need to list all numbers that are NOT contained in that set. Ã =. Set B = {Numbers greater than or equal to zero} The complement of set B will contain numbers that are greater than or equal to zero. So, Or, Or, =. =. =.

7 7 Set R = {The days it rained in Seattle, WA in 2006}. Set S = {The days it snowed in Seattle, WA in 2006}. Set N = {The days it both rained and snowed in Seattle, WA in 2006}. =. = = Now, do the practice problems and seek help if needed.

8 Cross Products of Sets The cross product of two sets results in. The first element of each pair is. The second element of each pair is. Cross product of sets is identified by what symbol?. Set A = {Salami, Ham} and Set B = {White, Wheat, Rye} To begin, we take the element from the first set and pair it with element from the second set. Next, we take the element from the first set and pair it with element of the second set. A X B =. There are possible combinations. Set C = {1, 2, 3, 4, 5} and Set D = {r, s, t, l, n, e}. C X D = There are possible combinations. Gina is getting ready for her date tonight and cannot decide exactly what to wear. She has narrowed her choices down to three different pair of pants to choose from and 4 different tops. Here are her choices of each: Set P represents her pants choices, P = {White, Black, Denim} Set S represents her shirt choices by sleeve type, S = {Long, Short, Tank, Spaghetti} P X S = There are possible combinations. Remember, A X B does not equal B X A! It has to be done in the order asked for. Now, do the practice problems and seek help if needed.

9 9 Module Recap The of two sets results in a new third set that contains only the elements that both sets have in common. The word is represented by the symbol. The of two sets results in a new third set that contains all elements of both sets. The word is represented by the symbol U. are useful when you can list all the elements of each set in consideration. A is a collection of numbers or objects. These numbers or objects are called of the set. A set that has no members is called an and can be written as or. The of a set is the set of everything NOT contained in the given set. We will represent the of set A using the symbol Ã. Placing a line over the set name can represent the complement of any set. The of two sets is denoted by using the symbol X and results in a new third set that contains elements that are pairs. In a, the first element of each pair is an element in the first set; the second element of each pair is an element of the second set.