{"id":874,"date":"2016-12-19T21:20:22","date_gmt":"2016-12-19T21:20:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=874"},"modified":"2024-08-10T19:49:59","modified_gmt":"2024-08-10T19:49:59","slug":"logical-fallacies-in-common-language","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/coloradomesa-mathforliberalartscorequisite\/chapter\/logical-fallacies-in-common-language\/","title":{"raw":"4.2 Logical Fallacies in Common Language","rendered":"4.2 Logical Fallacies in Common Language"},"content":{"raw":"<h1>Introduction<\/h1>\r\n<h2>What you\u2019ll learn to do: Identify logical inconsistencies in every day language found in social media, politics, advertising, etc.<\/h2>\r\nIn our current, social media-driven society, we are exposed to many ideas, opinions, and arguments, many of which are not based in fact nor logic.\u00a0 It is important that, as consumers of information, we are able to sift through what is true and what is not as well as what constitutes a legitimate logical argument.\u00a0 In this section, we investigate some of the more common logical fallacies.\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify logical fallacies in common language including appeal to ignorance, appeal to authority, appeal to consequence, correlation implies causation, and straw man arguments.<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<h1>Logical Arguments and Fallacies<\/h1>\r\nWe begin with several key definitions.\r\n<div class=\"textbox examples\">\r\n<h3>Definitions<\/h3>\r\n<strong>Logic<\/strong> is the study of the methods and formal principles of reasoning.\r\n\r\nAn <strong>argument<\/strong> uses a set of facts or assumptions, called\u00a0<strong>premises<\/strong>, to proceed toward a conclusion via logical inferences (or reasoning).\r\n\r\nA <strong>fallacy<\/strong> is a deceptive argument in which a conclusion is reached based on a faulty or insufficient premise or faulty reasoning.\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>A Note about Logical Fallacies<\/h3>\r\nThe ideas sampled on this page are classic and are often found in irresponsible advertising, politics, and in social media.\u00a0 Many social media arguments appeal to emotion and sentiment.\u00a0 Political candidates often (sometimes unintentionally) employ one or more of these fallacies to favorably manipulate situation.\u00a0 A good way to understand them is to see as many examples of them in the world as you can.\u00a0 Consider the example that follows each fallacy and try to identify why the statement is indeed an example of the given fallacy.\u00a0 In many cases, a possible correction is offered.\u00a0 Do any of these corrections introduce other possible fallacies?\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n<div class=\"textbox\">\r\n<h3>Correlation implies causation<\/h3>\r\nThis fallacy assumes that just because two things are related one must have caused the other. Often there is a third variable not considered.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n<strong>Example<\/strong>\r\n\r\n\u201cMonths with high ice cream sales also have a high rate of deaths by drowning. Therefore ice cream must be causing people to drown.\u201d\r\n\r\n[reveal-answer q=\"51614\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"51614\"]This argument is implying a causal relation, when really both are more likely dependent on the weather; that ice cream and drowning are both more likely during warm summer months.[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox\">\r\n<h3>Ad hominem<\/h3>\r\nAn <strong>ad hominem argument<\/strong> attacks the person making the argument, ignoring the argument itself.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Ad Hominem Fallacy<\/h3>\r\n<strong>Example<\/strong>\r\n\r\n\u201cJane says that whales are fish, but she\u2019s only in the second grade, so she can\u2019t be right.\u201d\r\n[reveal-answer q=\"683444\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"683444\"]\r\n\r\nHere the argument is attacking Jane, not the validity of her claim, so this is an ad hominem argument.\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<strong>Possible Correction<\/strong>\r\n\r\n\u201cJane says that whales are fish, but everyone knows that they\u2019re really mammals\u2014she doesn't know what she's talking about.\u201d\r\n[reveal-answer q=\"421872\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"421872\"]This certainly isn\u2019t very nice, but it is <em>not<\/em> ad hominem since a valid counterargument is made along with the personal insult.[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox\">\r\n<h3>Appeal to ignorance<\/h3>\r\nAn\u00a0<strong>appeal to ignorance<\/strong>\u00a0argument assumes something is true because it hasn\u2019t been proven false.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Appeal to Ignorance<\/h3>\r\n<strong>Example<\/strong>\r\n\r\n\u201cNobody has proven that photo isn\u2019t Bigfoot, so it must be Bigfoot.\u201d\r\n\r\n[reveal-answer q=\"195885\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"195885\"]There is no proof that it is or is not Bigfoot so no conclusion can be made. [\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<strong>Possible Correction<\/strong>\r\n\r\n\u201cAfter performing photo-enhancement and analysis, it was determined that the creature in the photograph is a large bear. Therefore, it cannot be Bigfoot.\u201d\r\n\r\n[reveal-answer q=\"321194\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"321194\"]There is evidence to prove that the creature is a bear, therefore, it is logical to conclude that it is not Bigfoot.[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox\">\r\n<h3>Appeal to authority<\/h3>\r\n<strong>Appeal to authority<\/strong> arguments attempt to use the authority of a person to prove a claim. While often authority can provide strength to an argument, problems can occur when the person\u2019s opinion is not shared by other experts, or when the authority is irrelevant to the claim.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Appeal to authority<\/h3>\r\n<strong>Example 1<\/strong>\r\n\r\n\u201cA diet high in bacon can be healthy \u2013 Dr. Atkins said so.\u201d\r\n[reveal-answer q=\"536253\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"536253\"]Here, an appeal to the authority of a doctor is used for the argument. This generally would provide strength to the argument, except that the opinion that eating a diet high in saturated fat runs counter to general medical opinion. More supporting evidence would be needed to justify this claim.[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<strong>Example 2<\/strong>\r\n\r\n\u201cJennifer Hudson lost weight with Weight Watchers, so their program must work.\u201d\r\n\r\n[reveal-answer q=\"764781\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"764781\"]\r\n\r\nHere, there is an appeal to the authority of a celebrity. While her experience does provide evidence, it provides no more than any other person\u2019s experience would and a single data point is insufficient to support the claim that the program works.\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<strong>Example 2 Possible Correction<\/strong>\r\n\r\n\u201cAccording to Dr. Brunilda Nazario, Family Medicene Specialist and Lead Medical Director at WebMD, 'WW is one of the most well-researched weight loss programs available. And yes, it works. Many studies have shown that the plan can help you lose weight and keep it off. For instance, a study from The American Journal of Medicine showed that people doing WW lost more weight than those trying to drop pounds on their own. So the Weight Watcher program does work.\u201d\r\n\r\n[reveal-answer q=\"858367\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"858367\"]Here, the appeal is to a medical authority who cites a study in a well-respected medical journal.[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox\">\r\n<h3>Appeal to Consequence<\/h3>\r\nAn <strong>appeal to consequence<\/strong> concludes that a premise is true or false based on whether the consequences are desirable or not.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Appeal to Consequence<\/h3>\r\n<strong>Example<\/strong>\r\n\r\n\u201cHumans will travel faster than light because faster-than-light travel would be beneficial for space travel.\u201d\r\n\r\n[reveal-answer q=\"458369\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"458369\"]Although \"faster-than-light\" travel would certainly enhance our space travel, that does not guarantee that humans will be able to do it.[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox\">\r\n<h3>Straw man<\/h3>\r\nA <strong>straw man<\/strong> argument involves misrepresenting the argument in a less favorable way to make it easier to attack.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Straw Man<\/h3>\r\n<strong>Example<\/strong>\r\n\r\n\u201cSenator Jones has proposed reducing military funding by 10%. Apparently he wants to leave us defenseless against attacks by terrorists\u201d\r\n\r\n[reveal-answer q=\"105595\"]Show Discussion[\/reveal-answer]\r\n[hidden-answer a=\"105595\"]Here the arguer has represented a 10% funding cut as equivalent to leaving us defenseless.\u00a0 While this conclusion is a misrepresentation that does not logically follow, certainly most U.S. citizens would not want our country to be defenseless.\u00a0 Thus, equating the two statements makes it easier to attack Senator Jones.[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nHere are some examples for you to try:\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]206044[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]206046[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]206045[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5362\/2020\/04\/21003253\/Stop-S2021.png\"><img class=\"aligncenter size-full wp-image-6286\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5362\/2020\/04\/21003253\/Stop-S2021.png\" alt=\"\" width=\"488\" height=\"467\" \/><\/a>","rendered":"<h1>Introduction<\/h1>\n<h2>What you\u2019ll learn to do: Identify logical inconsistencies in every day language found in social media, politics, advertising, etc.<\/h2>\n<p>In our current, social media-driven society, we are exposed to many ideas, opinions, and arguments, many of which are not based in fact nor logic.\u00a0 It is important that, as consumers of information, we are able to sift through what is true and what is not as well as what constitutes a legitimate logical argument.\u00a0 In this section, we investigate some of the more common logical fallacies.<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Identify logical fallacies in common language including appeal to ignorance, appeal to authority, appeal to consequence, correlation implies causation, and straw man arguments.<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<h1>Logical Arguments and Fallacies<\/h1>\n<p>We begin with several key definitions.<\/p>\n<div class=\"textbox examples\">\n<h3>Definitions<\/h3>\n<p><strong>Logic<\/strong> is the study of the methods and formal principles of reasoning.<\/p>\n<p>An <strong>argument<\/strong> uses a set of facts or assumptions, called\u00a0<strong>premises<\/strong>, to proceed toward a conclusion via logical inferences (or reasoning).<\/p>\n<p>A <strong>fallacy<\/strong> is a deceptive argument in which a conclusion is reached based on a faulty or insufficient premise or faulty reasoning.<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>A Note about Logical Fallacies<\/h3>\n<p>The ideas sampled on this page are classic and are often found in irresponsible advertising, politics, and in social media.\u00a0 Many social media arguments appeal to emotion and sentiment.\u00a0 Political candidates often (sometimes unintentionally) employ one or more of these fallacies to favorably manipulate situation.\u00a0 A good way to understand them is to see as many examples of them in the world as you can.\u00a0 Consider the example that follows each fallacy and try to identify why the statement is indeed an example of the given fallacy.\u00a0 In many cases, a possible correction is offered.\u00a0 Do any of these corrections introduce other possible fallacies?<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox\">\n<h3>Correlation implies causation<\/h3>\n<p>This fallacy assumes that just because two things are related one must have caused the other. Often there is a third variable not considered.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p><strong>Example<\/strong><\/p>\n<p>\u201cMonths with high ice cream sales also have a high rate of deaths by drowning. Therefore ice cream must be causing people to drown.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q51614\">Show Discussion<\/span><\/p>\n<div id=\"q51614\" class=\"hidden-answer\" style=\"display: none\">This argument is implying a causal relation, when really both are more likely dependent on the weather; that ice cream and drowning are both more likely during warm summer months.<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox\">\n<h3>Ad hominem<\/h3>\n<p>An <strong>ad hominem argument<\/strong> attacks the person making the argument, ignoring the argument itself.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Ad Hominem Fallacy<\/h3>\n<p><strong>Example<\/strong><\/p>\n<p>\u201cJane says that whales are fish, but she\u2019s only in the second grade, so she can\u2019t be right.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q683444\">Show Discussion<\/span><\/p>\n<div id=\"q683444\" class=\"hidden-answer\" style=\"display: none\">\n<p>Here the argument is attacking Jane, not the validity of her claim, so this is an ad hominem argument.\n<\/p><\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong>Possible Correction<\/strong><\/p>\n<p>\u201cJane says that whales are fish, but everyone knows that they\u2019re really mammals\u2014she doesn&#8217;t know what she&#8217;s talking about.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q421872\">Show Discussion<\/span><\/p>\n<div id=\"q421872\" class=\"hidden-answer\" style=\"display: none\">This certainly isn\u2019t very nice, but it is <em>not<\/em> ad hominem since a valid counterargument is made along with the personal insult.<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox\">\n<h3>Appeal to ignorance<\/h3>\n<p>An\u00a0<strong>appeal to ignorance<\/strong>\u00a0argument assumes something is true because it hasn\u2019t been proven false.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Appeal to Ignorance<\/h3>\n<p><strong>Example<\/strong><\/p>\n<p>\u201cNobody has proven that photo isn\u2019t Bigfoot, so it must be Bigfoot.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q195885\">Show Discussion<\/span><\/p>\n<div id=\"q195885\" class=\"hidden-answer\" style=\"display: none\">There is no proof that it is or is not Bigfoot so no conclusion can be made. <\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong>Possible Correction<\/strong><\/p>\n<p>\u201cAfter performing photo-enhancement and analysis, it was determined that the creature in the photograph is a large bear. Therefore, it cannot be Bigfoot.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q321194\">Show Discussion<\/span><\/p>\n<div id=\"q321194\" class=\"hidden-answer\" style=\"display: none\">There is evidence to prove that the creature is a bear, therefore, it is logical to conclude that it is not Bigfoot.<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox\">\n<h3>Appeal to authority<\/h3>\n<p><strong>Appeal to authority<\/strong> arguments attempt to use the authority of a person to prove a claim. While often authority can provide strength to an argument, problems can occur when the person\u2019s opinion is not shared by other experts, or when the authority is irrelevant to the claim.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Appeal to authority<\/h3>\n<p><strong>Example 1<\/strong><\/p>\n<p>\u201cA diet high in bacon can be healthy \u2013 Dr. Atkins said so.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q536253\">Show Discussion<\/span><\/p>\n<div id=\"q536253\" class=\"hidden-answer\" style=\"display: none\">Here, an appeal to the authority of a doctor is used for the argument. This generally would provide strength to the argument, except that the opinion that eating a diet high in saturated fat runs counter to general medical opinion. More supporting evidence would be needed to justify this claim.<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong>Example 2<\/strong><\/p>\n<p>\u201cJennifer Hudson lost weight with Weight Watchers, so their program must work.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q764781\">Show Discussion<\/span><\/p>\n<div id=\"q764781\" class=\"hidden-answer\" style=\"display: none\">\n<p>Here, there is an appeal to the authority of a celebrity. While her experience does provide evidence, it provides no more than any other person\u2019s experience would and a single data point is insufficient to support the claim that the program works.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong>Example 2 Possible Correction<\/strong><\/p>\n<p>\u201cAccording to Dr. Brunilda Nazario, Family Medicene Specialist and Lead Medical Director at WebMD, &#8216;WW is one of the most well-researched weight loss programs available. And yes, it works. Many studies have shown that the plan can help you lose weight and keep it off. For instance, a study from The American Journal of Medicine showed that people doing WW lost more weight than those trying to drop pounds on their own. So the Weight Watcher program does work.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q858367\">Show Discussion<\/span><\/p>\n<div id=\"q858367\" class=\"hidden-answer\" style=\"display: none\">Here, the appeal is to a medical authority who cites a study in a well-respected medical journal.<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox\">\n<h3>Appeal to Consequence<\/h3>\n<p>An <strong>appeal to consequence<\/strong> concludes that a premise is true or false based on whether the consequences are desirable or not.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Appeal to Consequence<\/h3>\n<p><strong>Example<\/strong><\/p>\n<p>\u201cHumans will travel faster than light because faster-than-light travel would be beneficial for space travel.\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q458369\">Show Discussion<\/span><\/p>\n<div id=\"q458369\" class=\"hidden-answer\" style=\"display: none\">Although &#8220;faster-than-light&#8221; travel would certainly enhance our space travel, that does not guarantee that humans will be able to do it.<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox\">\n<h3>Straw man<\/h3>\n<p>A <strong>straw man<\/strong> argument involves misrepresenting the argument in a less favorable way to make it easier to attack.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Straw Man<\/h3>\n<p><strong>Example<\/strong><\/p>\n<p>\u201cSenator Jones has proposed reducing military funding by 10%. Apparently he wants to leave us defenseless against attacks by terrorists\u201d<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q105595\">Show Discussion<\/span><\/p>\n<div id=\"q105595\" class=\"hidden-answer\" style=\"display: none\">Here the arguer has represented a 10% funding cut as equivalent to leaving us defenseless.\u00a0 While this conclusion is a misrepresentation that does not logically follow, certainly most U.S. citizens would not want our country to be defenseless.\u00a0 Thus, equating the two statements makes it easier to attack Senator Jones.<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Here are some examples for you to try:<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm206044\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=206044&theme=oea&iframe_resize_id=ohm206044&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm206046\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=206046&theme=oea&iframe_resize_id=ohm206046&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm206045\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=206045&theme=oea&iframe_resize_id=ohm206045&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5362\/2020\/04\/21003253\/Stop-S2021.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6286\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5362\/2020\/04\/21003253\/Stop-S2021.png\" alt=\"\" width=\"488\" height=\"467\" \/><\/a><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-874\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Math in society. <strong>Authored by<\/strong>: Lippman, David. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Question ID 25481, 25482, 25483. <strong>Authored by<\/strong>: Lippman, David. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Math in society\",\"author\":\"Lippman, 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