2_f_Counting_Principles

2_f_Counting_Principles - */SETS /*/AND/*/ COUNTING...

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*/SETS /**/AND/**/ COUNTING PRINCIPLES/* 1) Describe what a set is and how sets are denoted. 2) Give examples of collections that are sets. 3) Give examples of collections that are not sets. 4) Describe empty sets, the associated symbols, and give examples of empty sets. 5) Describe subsets and give examples. 6) Define the cardinality of a set, its symbolic form, and give examples. 7) Define power set and its cardinality. 8) Write the members of the power set of the sets (i.e., list all possible subsets of): a) {A, B} b) {A, B, C} c) {A, B, C, D} d) {A, B, C, D, E} Do part d) for HW. Results published online. SUBSETS: f, {A}, {B}, {C}, {D}, {E}, {A,B}, {A,C}, {A,D}, {A,E}, {B,C}, {B,D}, {B,E}, {C,D}, {C,E}, {D,E}, {A,B,C}, {A,B,D}, {A,B,E}, {A,C,D}, {A,C,E), {A,D,E}, {B,C,D}, {B,C,E}, {B,D,E}, {C,D,E}, {A,B,C,D}, {A,B,C,E}, {A,B,D,E}, {A,C,D,E}, {B,C,D,E}, {A,B,C,D,E}. There are _ subsets. 9) Fundamental multiplication principle of mathematics a) AN EXAMPLE: Consider the sets E = {a, b, c} and F = {1, 2}. Write out all possible pairs of elements in such a way that the first element is from set E and the second element is from set F. Construct a tree diagram and a matrix. TREE DIAGRAM ORDERED PAIRS
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root F MATRIX E
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b) Statement: For two events _ , _ that occur in succession. 10) A person wants to purchase a cellular phone and a calling plan. Suppose that there are two choices of cellular phones (the Motorola and the Nokia) and three choices of calling plans (one for $29.99 which allows 300 minutes of airtime per month, a second for $39.99 which allows 600 minutes of airtime per month, and a third for $49.99 which allows 1000 minutes of airtime per month). In how many different ways can this person purchase a cellular phone and a calling plan? Show all possibilities using a matrix and using a tree diagram. 11) A game consists of tossing a coin and then rolling a die. How many different outcomes are possible? Show all possible outcomes using a matrix and using a tree diagram. 12) A particular kind of code consists of two digits. Each digit is one number from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. How many different two-digit codes are possible? Show all possible outcomes using a matrix and using a tree diagram. 13) State the general multiplication principle. 14) At a particular restaurant, customers can order a meal consisting of one choice of {steak, chicken, fish}, plus one choice of {baked potato, mashed potatoes}, plus one choice of {water, soda, juice}. In how many different ways can a customer order a meal? 15) A certain model of vehicle is available in twelve different colors, four different styles {hatchback, sedan, SUV, or station wagon}, {manual or automatic transmission}, and {two-door or four-door}. How many different possible choices of this vehicle are there? 16) A pizza can be ordered with four choices of size {small, medium,
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2_f_Counting_Principles - */SETS /*/AND/*/ COUNTING...

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