{"id":6835,"date":"2021-12-31T18:36:00","date_gmt":"2021-12-31T18:36:00","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/?post_type=chapter&#038;p=6835"},"modified":"2025-08-30T01:06:24","modified_gmt":"2025-08-30T01:06:24","slug":"1-5-applications-of-venn-diagrams","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/chapter\/1-5-applications-of-venn-diagrams\/","title":{"raw":"1.5 Applications of Venn Diagrams","rendered":"1.5 Applications of Venn Diagrams"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3 style=\"padding-left: 30px;\">Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Applications (surveys) of Venn diagrams with 2 sets<\/li>\r\n \t<li>Applications (surveys) of Venn diagrams with 3 sets<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n\r\n<strong>Applications of Venn Diagrams with Two Sets<\/strong>\r\n<div class=\"textbox examples\">\r\n<h3>EXAMPLE<\/h3>\r\nFor example, suppose you gave a survey and found that 15 people liked only dogs, 10 people liked only cats, and 40 people liked both dogs and cats. The Venn diagram would consist of two circles, one labeled dogs and one labeled cats.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204347\/DogsCats.jpg\"><img class=\"size-medium wp-image-6439 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204347\/DogsCats-300x222.jpg\" alt=\"\" width=\"300\" height=\"222\" \/><\/a>\r\n\r\nNotice that if you look at the set of those who like dogs, you will see there are 15 who like dogs only, and 40 who like both. The total number of people who like dogs is the sum of 15 and 40, which is 55.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204402\/dogcats4.jpg\"><img class=\"size-medium wp-image-6440 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204402\/dogcats4-300x260.jpg\" alt=\"\" width=\"300\" height=\"260\" \/><\/a>\r\n\r\nLikewise, if you look at the set of those who like cats, you will see there are 10 who like cats only, and 40 who like both. The total number of people who like cats is the sum of 40 and 10, which is 50.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204413\/dogscats5.jpg\"><img class=\"size-medium wp-image-6441 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204413\/dogscats5-290x300.jpg\" alt=\"\" width=\"290\" height=\"300\" \/><\/a>\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nA survey asks 200 people \u201cWhat beverage do you drink in the morning\u201d, and offers choices:\r\n<ul>\r\n \t<li>Tea only<\/li>\r\n \t<li>Coffee only<\/li>\r\n \t<li>Both coffee and tea<\/li>\r\n<\/ul>\r\nSuppose 20 report tea only, 80 report coffee only, 40 report both.\u00a0\u00a0 How many people drink tea in the morning? How many people drink neither tea or coffee?\r\n[reveal-answer q=\"432276\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"432276\"]\r\n\r\nThis question can most easily be answered by creating a Venn diagram. We can see that we can find the people who drink tea by adding those who drink only tea to those who drink both: 60 people.\r\n\r\nWe can also see that those who drink neither are those not contained in the any of the three other groupings, so we can count those by subtracting from the cardinality of the universal set, 200.\r\n\r\n200 \u2013 20 \u2013 80 \u2013 40 = 60 people who drink neither.\r\n\r\n<img class=\"alignnone size-full wp-image-458\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12222016\/coffeetea.png\" alt=\"coffeetea\" width=\"180\" height=\"124\" \/>\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\n[ohm_question]125872[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\nSuppose you asked 100 people if they like Star Wars or Star Trek.\r\n<ul>\r\n \t<li>32 like both<\/li>\r\n \t<li>40 liked just Star Wars<\/li>\r\n \t<li>20 liked just Star Trek<\/li>\r\n \t<li>8 liked neither<\/li>\r\n<\/ul>\r\nWe can fill in a Venn diagram with this information. First, start with the general format for two sets:\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18160316\/blank-venn-diagram-2-circles.png\"><img class=\"size-medium wp-image-5377 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18160316\/blank-venn-diagram-2-circles-300x259.png\" alt=\"\" width=\"300\" height=\"259\" \/><\/a>\r\n\r\nThen, fill in the number in the intersection.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161248\/venn-diagram-1.png\"><img class=\"size-medium wp-image-5378 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161248\/venn-diagram-1-300x190.png\" alt=\"\" width=\"300\" height=\"190\" \/><\/a>\r\n\r\nFill in the \"just Star Wars\", \"just Star Trek\", and neither areas.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161456\/venn-diagram-2.png\"><img class=\"size-medium wp-image-5379 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161456\/venn-diagram-2-300x189.png\" alt=\"\" width=\"300\" height=\"189\" \/><\/a>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\nAnother, slightly harder example. Suppose you conducted a survey and asked 50 people if they liked Popeye's chicken sandwich or Wendy's chicken sandwich. You found:\r\n12 liked both\r\n30 liked Popeye's\r\n14 liked Wendy's\r\n\r\nStart with your blank Venn Diagram.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18160316\/blank-venn-diagram-2-circles.png\"><img class=\"size-medium wp-image-5377 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18160316\/blank-venn-diagram-2-circles-300x259.png\" alt=\"\" width=\"300\" height=\"259\" \/><\/a>\r\n\r\nNext, like before, fill in the intersection.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161757\/Venn-diagram-3.png\"><img class=\"size-medium wp-image-5380 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161757\/Venn-diagram-3-300x191.png\" alt=\"\" width=\"300\" height=\"191\" \/><\/a>\r\n\r\nThe wording was a little different in this example. Note, we know the TOTAL number of people who liked Popeye's. We will need to subtract off the overlap in order to find out how many people liked just Popeye's. So, 30-12=18. Put this in your diagram.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161940\/Venn-diagram-4.png\"><img class=\"size-medium wp-image-5381 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161940\/Venn-diagram-4-300x190.png\" alt=\"\" width=\"300\" height=\"190\" \/><\/a>\r\n\r\nDo the same thing with Wendy's, subtract off the intersection to find out how many people just like Wendy's.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162049\/Venn-diagram-5.png\"><img class=\"size-medium wp-image-5382 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162049\/Venn-diagram-5-300x191.png\" alt=\"\" width=\"300\" height=\"191\" \/><\/a>\r\n\r\nFinally, add all of the numbers in the circles and overlap. This is how many people answered that they liked either Popeye's or Wendy's or both. Subtract this number from the total surveyed. We have 50-32=18. Put this in the diagram outside of the circles.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162218\/Venn-diagram-6.png\"><img class=\"size-medium wp-image-5383 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162218\/Venn-diagram-6-300x190.png\" alt=\"\" width=\"300\" height=\"190\" \/><\/a>\r\n\r\n<\/div>\r\n<div><strong>Applications of Venn Diagrams with Three Sets<\/strong><\/div>\r\n<div>What about a diagram with three sets? You can do it much the same as the Venn diagrams with two sets. The key is to start in the middle and work your way out.<\/div>\r\n<p style=\"text-align: center;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162449\/venn-blank-3circles.png\"><img class=\"wp-image-5384 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162449\/venn-blank-3circles-300x204.png\" alt=\"\" width=\"399\" height=\"271\" \/><\/a><\/p>\r\n\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\nSuppose you surveyed a group of 160 people who ordered pizza from Pizza Hut and asked them what they ordered.\r\n150 ordered pizza\r\n80 ordered bread sticks\r\n90 ordered soda\r\n50 ordered pizza and bread sticks (no soda)\r\n70 ordered pizza and soda (no bread sticks)\r\n0 ordered bread sticks and soda (no pizza)\r\n20 ordered all three\r\n<div><\/div>\r\nStart in the middle and work your way out. So start with 20 who ordered all three.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18163159\/venn-3-diagram-1.png\"><img class=\"size-medium wp-image-5386 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18163159\/venn-3-diagram-1-300x204.png\" alt=\"\" width=\"300\" height=\"204\" \/><\/a>\r\n\r\nNext, add in where two sets overlap.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18163752\/venn-3-diagram-2.png\"><img class=\"size-medium wp-image-5387 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18163752\/venn-3-diagram-2-300x202.png\" alt=\"\" width=\"300\" height=\"202\" \/><\/a>\r\n\r\nNext, you want to find out how many ordered JUST pizza, JUST soda, and JUST bread sticks. We know that 150 ordered pizza, so take 150 and subtract off the numbers already in the pizza circle (50, 20, and 70). You should get 10. Do this with soda and bread sticks as well, and add your results to the Venn diagram.\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18164055\/venn-3-diagram-3.png\"><img class=\"size-medium wp-image-5388 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18164055\/venn-3-diagram-3-300x204.png\" alt=\"\" width=\"300\" height=\"204\" \/><\/a>\r\n\r\nFinally, you want to figure out if there is anyone in the universal set (the 160 asked) who did not order pizza, bread sticks, or soda. You want to add all the numbers in the circles and subtract this from 160. 160- (10+50+20+70+10+0+0)= 160-160=0\r\n\r\nWe do not have any members who need to be accounted for outside of the circles.\r\n\r\n<\/div>\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 style=\"padding-left: 30px;\">Learning Objectives<\/h3>\n<ul>\n<li>Applications (surveys) of Venn diagrams with 2 sets<\/li>\n<li>Applications (surveys) of Venn diagrams with 3 sets<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<p><strong>Applications of Venn Diagrams with Two Sets<\/strong><\/p>\n<div class=\"textbox examples\">\n<h3>EXAMPLE<\/h3>\n<p>For example, suppose you gave a survey and found that 15 people liked only dogs, 10 people liked only cats, and 40 people liked both dogs and cats. The Venn diagram would consist of two circles, one labeled dogs and one labeled cats.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204347\/DogsCats.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-6439 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204347\/DogsCats-300x222.jpg\" alt=\"\" width=\"300\" height=\"222\" \/><\/a><\/p>\n<p>Notice that if you look at the set of those who like dogs, you will see there are 15 who like dogs only, and 40 who like both. The total number of people who like dogs is the sum of 15 and 40, which is 55.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204402\/dogcats4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-6440 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204402\/dogcats4-300x260.jpg\" alt=\"\" width=\"300\" height=\"260\" \/><\/a><\/p>\n<p>Likewise, if you look at the set of those who like cats, you will see there are 10 who like cats only, and 40 who like both. The total number of people who like cats is the sum of 40 and 10, which is 50.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204413\/dogscats5.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-6441 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/25204413\/dogscats5-290x300.jpg\" alt=\"\" width=\"290\" height=\"300\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>A survey asks 200 people \u201cWhat beverage do you drink in the morning\u201d, and offers choices:<\/p>\n<ul>\n<li>Tea only<\/li>\n<li>Coffee only<\/li>\n<li>Both coffee and tea<\/li>\n<\/ul>\n<p>Suppose 20 report tea only, 80 report coffee only, 40 report both.\u00a0\u00a0 How many people drink tea in the morning? How many people drink neither tea or coffee?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q432276\">Show Solution<\/span><\/p>\n<div id=\"q432276\" class=\"hidden-answer\" style=\"display: none\">\n<p>This question can most easily be answered by creating a Venn diagram. We can see that we can find the people who drink tea by adding those who drink only tea to those who drink both: 60 people.<\/p>\n<p>We can also see that those who drink neither are those not contained in the any of the three other groupings, so we can count those by subtracting from the cardinality of the universal set, 200.<\/p>\n<p>200 \u2013 20 \u2013 80 \u2013 40 = 60 people who drink neither.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-458\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/276\/2016\/10\/12222016\/coffeetea.png\" alt=\"coffeetea\" width=\"180\" height=\"124\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm125872\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=125872&theme=oea&iframe_resize_id=ohm125872&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p>Suppose you asked 100 people if they like Star Wars or Star Trek.<\/p>\n<ul>\n<li>32 like both<\/li>\n<li>40 liked just Star Wars<\/li>\n<li>20 liked just Star Trek<\/li>\n<li>8 liked neither<\/li>\n<\/ul>\n<p>We can fill in a Venn diagram with this information. First, start with the general format for two sets:<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18160316\/blank-venn-diagram-2-circles.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5377 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18160316\/blank-venn-diagram-2-circles-300x259.png\" alt=\"\" width=\"300\" height=\"259\" \/><\/a><\/p>\n<p>Then, fill in the number in the intersection.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161248\/venn-diagram-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5378 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161248\/venn-diagram-1-300x190.png\" alt=\"\" width=\"300\" height=\"190\" \/><\/a><\/p>\n<p>Fill in the &#8220;just Star Wars&#8221;, &#8220;just Star Trek&#8221;, and neither areas.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161456\/venn-diagram-2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5379 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161456\/venn-diagram-2-300x189.png\" alt=\"\" width=\"300\" height=\"189\" \/><\/a><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p>Another, slightly harder example. Suppose you conducted a survey and asked 50 people if they liked Popeye&#8217;s chicken sandwich or Wendy&#8217;s chicken sandwich. You found:<br \/>\n12 liked both<br \/>\n30 liked Popeye&#8217;s<br \/>\n14 liked Wendy&#8217;s<\/p>\n<p>Start with your blank Venn Diagram.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18160316\/blank-venn-diagram-2-circles.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5377 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18160316\/blank-venn-diagram-2-circles-300x259.png\" alt=\"\" width=\"300\" height=\"259\" \/><\/a><\/p>\n<p>Next, like before, fill in the intersection.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161757\/Venn-diagram-3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5380 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161757\/Venn-diagram-3-300x191.png\" alt=\"\" width=\"300\" height=\"191\" \/><\/a><\/p>\n<p>The wording was a little different in this example. Note, we know the TOTAL number of people who liked Popeye&#8217;s. We will need to subtract off the overlap in order to find out how many people liked just Popeye&#8217;s. So, 30-12=18. Put this in your diagram.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161940\/Venn-diagram-4.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5381 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18161940\/Venn-diagram-4-300x190.png\" alt=\"\" width=\"300\" height=\"190\" \/><\/a><\/p>\n<p>Do the same thing with Wendy&#8217;s, subtract off the intersection to find out how many people just like Wendy&#8217;s.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162049\/Venn-diagram-5.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5382 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162049\/Venn-diagram-5-300x191.png\" alt=\"\" width=\"300\" height=\"191\" \/><\/a><\/p>\n<p>Finally, add all of the numbers in the circles and overlap. This is how many people answered that they liked either Popeye&#8217;s or Wendy&#8217;s or both. Subtract this number from the total surveyed. We have 50-32=18. Put this in the diagram outside of the circles.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162218\/Venn-diagram-6.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5383 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162218\/Venn-diagram-6-300x190.png\" alt=\"\" width=\"300\" height=\"190\" \/><\/a><\/p>\n<\/div>\n<div><strong>Applications of Venn Diagrams with Three Sets<\/strong><\/div>\n<div>What about a diagram with three sets? You can do it much the same as the Venn diagrams with two sets. The key is to start in the middle and work your way out.<\/div>\n<p style=\"text-align: center;\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162449\/venn-blank-3circles.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-5384 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18162449\/venn-blank-3circles-300x204.png\" alt=\"\" width=\"399\" height=\"271\" \/><\/a><\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p>Suppose you surveyed a group of 160 people who ordered pizza from Pizza Hut and asked them what they ordered.<br \/>\n150 ordered pizza<br \/>\n80 ordered bread sticks<br \/>\n90 ordered soda<br \/>\n50 ordered pizza and bread sticks (no soda)<br \/>\n70 ordered pizza and soda (no bread sticks)<br \/>\n0 ordered bread sticks and soda (no pizza)<br \/>\n20 ordered all three<\/p>\n<div><\/div>\n<p>Start in the middle and work your way out. So start with 20 who ordered all three.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18163159\/venn-3-diagram-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5386 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18163159\/venn-3-diagram-1-300x204.png\" alt=\"\" width=\"300\" height=\"204\" \/><\/a><\/p>\n<p>Next, add in where two sets overlap.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18163752\/venn-3-diagram-2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5387 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18163752\/venn-3-diagram-2-300x202.png\" alt=\"\" width=\"300\" height=\"202\" \/><\/a><\/p>\n<p>Next, you want to find out how many ordered JUST pizza, JUST soda, and JUST bread sticks. We know that 150 ordered pizza, so take 150 and subtract off the numbers already in the pizza circle (50, 20, and 70). You should get 10. Do this with soda and bread sticks as well, and add your results to the Venn diagram.<br \/>\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18164055\/venn-3-diagram-3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-5388 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5548\/2021\/01\/18164055\/venn-3-diagram-3-300x204.png\" alt=\"\" width=\"300\" height=\"204\" \/><\/a><\/p>\n<p>Finally, you want to figure out if there is anyone in the universal set (the 160 asked) who did not order pizza, bread sticks, or soda. You want to add all the numbers in the circles and subtract this from 160. 160- (10+50+20+70+10+0+0)= 160-160=0<\/p>\n<p>We do not have any members who need to be accounted for outside of the circles.<\/p>\n<\/div>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">This is the end of the section. 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