{"id":6785,"date":"2021-12-30T21:37:33","date_gmt":"2021-12-30T21:37:33","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/?post_type=chapter&#038;p=6785"},"modified":"2022-01-06T22:17:07","modified_gmt":"2022-01-06T22:17:07","slug":"1-4-venn-diagrams","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/chapter\/1-4-venn-diagrams\/","title":{"raw":"1.4 Venn Diagrams","rendered":"1.4 Venn Diagrams"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Venn Diagrams for unions, intersections, and complements<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Venn Diagrams<\/h2>\r\nTo visualize the interaction of sets, John Venn in 1880 thought to use overlapping circles, building on a similar idea used by Leonhard Euler in the 18th century. These illustrations now called\u00a0<strong>Venn Diagrams<\/strong>.\r\n<div class=\"textbox\">\r\n<h3>VENN DIAGRAM<\/h3>\r\nA Venn diagram represents each set by a circle, usually drawn inside of a containing box representing the universal set. Overlapping areas indicate elements common to both sets.\r\n\r\nBasic Venn diagrams can illustrate the interaction of two or three sets.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nCreate Venn diagrams to illustrate <em>A <\/em>\u22c3<em> B<\/em>, <em>A <\/em>\u22c2<em> B<\/em>, and <em>A'\u00a0<\/em>\u22c2<em> B<\/em>\r\n\r\n<em>A <\/em>\u22c3<em> B<\/em> contains all elements in <em>either<\/em> set.\r\n[reveal-answer q=\"252649\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"252649\"]\r\n\r\n<img class=\"alignnone size-full wp-image-449\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220329\/ab1.png\" alt=\"ab1\" width=\"179\" height=\"125\" \/>\r\n\r\n<em>A <\/em>\u22c2<em> B<\/em> contains only those elements in both sets \u2013 in the overlap of the circles.\r\n\r\n<img class=\"alignnone size-full wp-image-450\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220349\/ab2.png\" alt=\"ab2\" width=\"180\" height=\"125\" \/>\r\n\r\n<em>Ac <\/em>will contain all elements <em>not<\/em> in the set A. <em>A'<sup>\u00a0<\/sup><\/em>\u22c2<em> B<\/em> will contain the elements in set <em>B<\/em> that are not in set <em>A<\/em>.\r\n\r\n<img class=\"alignnone size-full wp-image-451\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220403\/ab3.png\" alt=\"ab3\" width=\"180\" height=\"125\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse a Venn diagram to illustrate (<em>H <\/em>\u22c2<em> F<\/em>)' \u22c2<em> W\r\n<\/em>[reveal-answer q=\"311976\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"311976\"]\r\n\r\nWe\u2019ll start by identifying everything in the set <em>H <\/em>\u22c2<em> F<\/em>\r\n\r\n<img class=\"alignnone wp-image-452 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220617\/hfw1.png\" alt=\"A Venn diagram depicting three overlapping circles, labeled H, F, and W, respectively. The area where H and F overlap is outlined in red.\" width=\"180\" height=\"152\" \/>\r\n\r\nNow, (<em>H <\/em>\u22c2<em> F<\/em>)' \u22c2<em> W<\/em> will contain everything <em>not<\/em> in the set identified above that is also in set <em>W<\/em>.\r\n\r\n<img class=\"alignnone wp-image-453 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220632\/hfw2.png\" alt=\"A Venn diagram depicting three overlapping circles, labeled H, F, and W, respectively. The area of circle W where it does not overlap with H and F at the same time is outlined in red.\" width=\"180\" height=\"156\" \/>\r\n\r\n&nbsp;\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/CPeeOUldZ6M\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nCreate an expression to represent the outlined part of the Venn diagram shown.\r\n\r\n<img class=\"alignnone size-full wp-image-454\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220943\/hfw3.png\" alt=\"hfw3\" width=\"180\" height=\"157\" \/>\r\n[reveal-answer q=\"828282\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"828282\"]\r\n\r\nThe elements in the outlined set <em>are<\/em> in sets <em>H<\/em> and <em>F<\/em>, but are not in set <em>W<\/em>. So we could represent this set as <em>H <\/em>\u22c2<em> F<\/em> \u22c2<em> W'<\/em>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nCreate an expression to represent the outlined portion of the Venn diagram shown.\r\n\r\n<img class=\"alignnone size-full wp-image-455\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12221621\/abc1.png\" alt=\"abc1\" width=\"180\" height=\"157\" \/>\r\n\r\n[ohm_question]6699[\/ohm_question]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/VfC8rhLdYYg\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/span><\/strong><\/p>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Venn Diagrams for unions, intersections, and complements<\/li>\n<\/ul>\n<\/div>\n<h2>Venn Diagrams<\/h2>\n<p>To visualize the interaction of sets, John Venn in 1880 thought to use overlapping circles, building on a similar idea used by Leonhard Euler in the 18th century. These illustrations now called\u00a0<strong>Venn Diagrams<\/strong>.<\/p>\n<div class=\"textbox\">\n<h3>VENN DIAGRAM<\/h3>\n<p>A Venn diagram represents each set by a circle, usually drawn inside of a containing box representing the universal set. Overlapping areas indicate elements common to both sets.<\/p>\n<p>Basic Venn diagrams can illustrate the interaction of two or three sets.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Create Venn diagrams to illustrate <em>A <\/em>\u22c3<em> B<\/em>, <em>A <\/em>\u22c2<em> B<\/em>, and <em>A&#8217;\u00a0<\/em>\u22c2<em> B<\/em><\/p>\n<p><em>A <\/em>\u22c3<em> B<\/em> contains all elements in <em>either<\/em> set.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q252649\">Show Solution<\/span><\/p>\n<div id=\"q252649\" class=\"hidden-answer\" style=\"display: none\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-449\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220329\/ab1.png\" alt=\"ab1\" width=\"179\" height=\"125\" \/><\/p>\n<p><em>A <\/em>\u22c2<em> B<\/em> contains only those elements in both sets \u2013 in the overlap of the circles.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-450\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220349\/ab2.png\" alt=\"ab2\" width=\"180\" height=\"125\" \/><\/p>\n<p><em>Ac <\/em>will contain all elements <em>not<\/em> in the set A. <em>A&#8217;<sup>\u00a0<\/sup><\/em>\u22c2<em> B<\/em> will contain the elements in set <em>B<\/em> that are not in set <em>A<\/em>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-451\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220403\/ab3.png\" alt=\"ab3\" width=\"180\" height=\"125\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use a Venn diagram to illustrate (<em>H <\/em>\u22c2<em> F<\/em>)&#8217; \u22c2<em> W<br \/>\n<\/em><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q311976\">Show Solution<\/span><\/p>\n<div id=\"q311976\" class=\"hidden-answer\" style=\"display: none\">\n<p>We\u2019ll start by identifying everything in the set <em>H <\/em>\u22c2<em> F<\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-452 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220617\/hfw1.png\" alt=\"A Venn diagram depicting three overlapping circles, labeled H, F, and W, respectively. The area where H and F overlap is outlined in red.\" width=\"180\" height=\"152\" \/><\/p>\n<p>Now, (<em>H <\/em>\u22c2<em> F<\/em>)&#8217; \u22c2<em> W<\/em> will contain everything <em>not<\/em> in the set identified above that is also in set <em>W<\/em>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-453 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220632\/hfw2.png\" alt=\"A Venn diagram depicting three overlapping circles, labeled H, F, and W, respectively. The area of circle W where it does not overlap with H and F at the same time is outlined in red.\" width=\"180\" height=\"156\" \/><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Sets: drawing a Venn diagram\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/CPeeOUldZ6M?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Create an expression to represent the outlined part of the Venn diagram shown.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-454\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12220943\/hfw3.png\" alt=\"hfw3\" width=\"180\" height=\"157\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q828282\">Show Solution<\/span><\/p>\n<div id=\"q828282\" class=\"hidden-answer\" style=\"display: none\">\n<p>The elements in the outlined set <em>are<\/em> in sets <em>H<\/em> and <em>F<\/em>, but are not in set <em>W<\/em>. So we could represent this set as <em>H <\/em>\u22c2<em> F<\/em> \u22c2<em> W&#8217;<\/em><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Create an expression to represent the outlined portion of the Venn diagram shown.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-455\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12221621\/abc1.png\" alt=\"abc1\" width=\"180\" height=\"157\" \/><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm6699\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=6699&theme=oea&iframe_resize_id=ohm6699&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Sets: writing an expression for a Venn diagram region\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/VfC8rhLdYYg?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">This is the end of the section. Close this tab and proceed to the corresponding assignment.<\/span><\/strong><\/p>\n","protected":false},"author":359705,"menu_order":5,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-6785","chapter","type-chapter","status-publish","hentry"],"part":159,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6785","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/users\/359705"}],"version-history":[{"count":9,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6785\/revisions"}],"predecessor-version":[{"id":6994,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6785\/revisions\/6994"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/parts\/159"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6785\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/media?parent=6785"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapter-type?post=6785"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/contributor?post=6785"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/license?post=6785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}