# MATC1100

 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } What are the two types of reasoning we use in everyday life? 1. Inductive reasoning2. Deductive reasoning inductive reasoning Inductive reasoning is the process of reasoning that arrives at a general conclusion or conjecture based on the observation of specific examples. **Using specific examples to --- arrive --- at a general conclusion deductive reasoning Deductive reasoning is the process of reasoning that arrives at a specific conclusion based on previously accepted general statements. ** Arrive at a specific conclusion --- via --- previously accepted statements. George Polya FOUR major steps of problem solving 1. Understand the problem2. Devise a plan3. Carry out the plan4. Look back, check the work estimation Estimation is the process of finding an approximate answer to a mathematical problem. In many cases, it is not necessary to find the exact answer to a problem. When only an approximate answer is needed, you can use estimation. This is accopmplished by rounding the numbers used in the problem, then performing the necessary operatioin or operations. define a set A set is a well-defined collection of objects/elements. What is meant when a set is well defined? A set is said to be well defined when there is no misunderstanding as to whether or not an element belongs to a set. Ex:the set of "letters of the English alphabet" is a well-defined set since it consists of the 26 symbols. The set of Great Lakes is {Ontario, Erie, Huron, Michigan, Superior}The days of the week are {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}Write the set of natural numbers less than 6 {1, 2, 3, 4, 5} Name the 3 ways to designate sets 1. list or roster method2. descriptive method3. set-builder method Each object of a set is called... an element or member of the set. Write the set of natural numbers less than 8. {1, 2, 3, 4, 5, 6, 7} Write the descriptive of the set containing 2, 4, 6, 8, ... Since the elements in the set are called the even natural numbers, the anser is: E = even natural numbers Use set-builder notation to designate the set {2, 4, 6} { x | x ∈ E and x < 7 } Reads: "The set of all x such that x is an even natural number and x is less than seven." Use set-builder notation to designate the set {red, yellow, blue} {x | x is a primary color} Reads: "The set of all x such that x is a primary color." Designate the set 32, 33, 34, 35, ... using the roster method. {32, 33, 34, 35, ...} Designate the set 32, 33, 34, 35, ... using the descriptive method. Natural numbers greater than 31. Designate the set 32, 33, 34, 35, ... using the set-builder notation. { x | x ∈ N and x > 31 } finite set A set is said to be a finite set if the number of elements contained in the set is either 0 or a natural number. infinite set A set is said to be an infinite set if it has an unlimited number of elements. finite? or infinte? {the natural numbers that are multiples of 6} infinite finite? or infinte? { x | x is a member of the U.S. Senate} finite finite? or infinte? {3, 6, 9, ..., 24} finite null set A set with no elements is called an empty set or null set. The symbols used to represent the null set are { } or circle w/line Two sets are equal if... they have exactly the same members or elements. Two sets have a one-to-one correspondence if and only if... it is possible to pair the elements of one set with the elements of the other set in such a way that for each element in the first set there exists one and only one element in the second set. What is a subset? When all, some, or none of the elements of one set are used in another set, the second set is called a subset of the original set. Formally defined. Ex: Subsets of {bacon, egg} {bacon, egg}{bacon}{egg}{ } What is a proper subset? If a subset of a given set is NOT equal to the original set, then the subset is called a proper subset of the original set. Original set: {bacon, egg} {bacon, egg} ⊄ {bacon, egg} **Because it is equal to the original {bacon}⊂ {bacon, egg} What is the union of two sets? All the elements of each set. Duplicates are not written twice. Ex: A={10, 12, 14, 15} and B={13, 14, 15, 16, 17} A ∪ B={10, 12, 13, 14, 15, 16, 17} What is the intersection of two sets? The set of elements that are common to both sets. Ex: A={10, 12, 14, 15} and B={13, 14, 15, 16, 17} A∩ B = {14, 15} What is the complement of a set? It is the set of elements contained in the universal set that are NOT contained in the set noted._A (the line over the set name denotes the compliment of that set)Basically everything outside of the mentioned set. What is a Venn Diagram? When a set or sets are represented pictorially using Venn Diagrams. .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Authorinsouci ID4347 Card SetMATC1100 DescriptionCh. 1&2 Updated2010-01-17T05:29:31Z Show Answers