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18 Cards in this Set
- Front
- Back
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What is a set
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A set is a group of objects Customers who dyed their hair blond, customers who dyed their eyebrows blonde, and customers who straightened their hair. This passage has 3 sets. |
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What is a sample space
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The sample space is the collection of all items from which the sets are chosen.
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Of the 120 parliament members in country [x], 35 belong to the Labor Party. 12 of the labor party members are women... How would you define the relations between the groups? |
A - All Parliament members B - Labor Party Members C - Woman in the Labor Party A is the sample space B is the set C is the subset |
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Using the previous example, what is a complimentary set
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When you have a set (set b=Labor party members) in a sample space (all parliament members) all members of the sample space which are not members of B comprise the complementary set to b
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Using the previous example, describe what a subset is?
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All members of the set C also belong to set B, then C is defined as the subset of B
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What are the sets is the following example: Looking at the menu of the Maple-Deli restaurant and 15 of the dishes are main courses and 25 dishes are vegetarian How many of the dishes are vegetarian main courses? |
Anywhere betwen 0 and 15 Set A - 15 dishes (main course) Set B - 24 dishes (vegetarian) The question asked how many dishes belong to Set A and to Set B. |
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What is an Intersection A ∩ B ? |
All items that belong to set A and to set B This is the definition of interesection between sets. |
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What is the sample space, set and subset of the below question: Of the 13 members of a book club, 5 of them finished reading at least 7 books over the summer. How many members of the book club finished fewer than 7 books over the summer? |
There were 5 members that finished reading at least 7 books. So, there were 13 - 5 = 8 members that did not finish reading at least 7 books. Sample space - 13 members Those that read at least 7 books - Set A Those that finished reading less than 7 - Compliment (b/c it contains all elements that are not in set A. |
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When are two sets complementary sets?
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If they do not have any members in common - In other words, they don't intersect and they include all members of the sample space.
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Of the 13 members of a book club, 5 of them have blond hair. How many members of the club have brown hair? What is the sample space? What is the set? What is the compliment? |
Can't anser the question definitively. Sample space - 13 members Set A - 5 have blond hair Compliment of Set A - members who don't have blond hair. |
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Joe's liquor store stocks only two brands of whiskey: "John Bar" and "Bark". 45 bottles of whiskey were sold today at Joe's, and 20 of them were "John Bar" brand. How many bottles of "Bark" whiskey were sold at Joe's today? What is the sample space? What is the set? What is the compliment? |
25 Sample Space - 45 bottles of whiskey Set A - John Bar Set B - Bark Compliment - Set B is the compliment to Set A in this example. Why? When a question states that every item in the sample space belongs to either set A or Set B, and no other option exists, then the other Set is the compliment to Set A. |
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Using the example below what is a Union? 18 of the guests at Danny's birthday party brought presents, and 11 of the guests did not. How many guests were at Danny's birthday party? |
29 Set A - 18 guests that brought a present Set B - 11 guests that didn't bring a present the union of sets is all the elements that are included in at least one of the sets. Since all members of the party are contained in these two sets, the total number of guests is equal to the union of Sets A and B. Union of A and B=A∪B |
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At that party (which included 29 guests) 12 guests ate fudge cake and 20 guests ate red velvet cake. If those were the only two cakes served, how many guests ate cake at the party? What is the sample space? What is the set? What is the subset? |
There is a range of answers because a guest can eat both types of cakes. Set A - Fudge Cakes (12 members) Set B - Red velvet cake (20 guests) Sample Space - 29 total guests |
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At that party (which included 29 guests) 12 guests ate fudge cake and 20 guests ate red velvet cake. 5 guests had both cakes. How many guests ate at least one type of cake? What are the sets? What is the sample space? What is the compliment |
Sample Space - 29 guests Set A - fudge cakes (12 guests) Set B - Red velvet cakes (20 guests) Intersection of A and B: A∩B= 5 who eat both cakes. The set of those that ate at least one type of cake: A∪B=[Only Fudge]+[Only Red Velvet]+[Both Cakes] - Now determine each peice of the equation |
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How to figure out how many ate fudge (Set A) and how many ate only Red Velvet (Set B)
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There are 7 guests that only fudge cake because the intersection is included in both sets. A = only Fudge (7) + both cakes (5) 12 = X + 5 x= 7 B = Only Red Velvet (15) + both Cakes (5) 20 = x + 5 x = 15 |
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Puttin the equation together: A∪B=[Only Fudge]+[Only Red Velvet]+[Both Cakes] ? |
A∪B=7+15+5=27
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Another way to describe Union of Sets
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Counting every item that belongs to at least on the sets In other words, the Union of A and B is all the items that belong to Set A or B (or both). It is written as A∪B. Therefore the Union is comprised of: A + only B + Intersection of A and B (both). |
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Using the Inclusion-Exclusion Principle, how can I calculate the Union of two sets ?
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Using the intersection of the two sets: A∪B = A + B - A∩B. |
