{"id":7035,"date":"2014-05-19T17:15:43","date_gmt":"2014-05-19T17:15:43","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=7035"},"modified":"2014-12-02T08:25:29","modified_gmt":"2014-12-02T08:25:29","slug":"math-review-of-intersection-and-union-of-sets","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/05\/19\/math-review-of-intersection-and-union-of-sets\/","title":{"rendered":"Math Review of Intersection and Union of Sets"},"content":{"rendered":"

Overview<\/h3>\n

The intersection of sets refers to the elements that both sets have in common, while the union of sets refers to the elements that both sets have together.\u00a0 If the sets are finite, the elements of the new set can be listed.\u00a0 Otherwise, they can be described graphically, algebraically, or by the rule that governs them.<\/p>\n

Intersection of Sets<\/h3>\n

Suppose that Set A has the elements {1, 3, 5, 7, 9, 11} and set B has the elements {2, 3, 4, 5, 6, 7}.\u00a0 The intersection of those sets would be {3, 5, 7}. If the sets were infinite rather than finite, the elements of the set couldn\u2019t be listed, so the rules for generating sets would need to be used.\u00a0 If set A were defined as {all odd integers} and set B were defined as {all integers greater than or equal to 2},\u00a0their intersection\u00a0would be described as {all odd integers greater than 2}.<\/p>\n\n\n\n
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Figure 1:\u00a0 A Venn diagram shows the relationship between sets.\u00a0In this diagram, the intersection between the sets is all odd integers greater than 2.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Combining Conditions<\/h3>\n

The principles of the intersection of sets can also be used to solve problems algebraically.\u00a0 Suppose that one plant grows best in a range of 30% to 50% sunlight and another plant grows best when it gets at least 45% sunlight.\u00a0 What is the range where both plants can grow best?\u00a0 Let s represent the percentage of sunlight.\u00a0 The first plant grows best at a range where 30>s<50, and the second plant 45<s. The second plant will not grow as well when s is between 30 and 45, and the first plant will not grow well if s is above 50%.\u00a0 Combining the two conditions, both plants will grow well when 45<s<50.<\/p>\n\n\n\n
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Figure 2: \u00a0Combining conditions will create an intersection type of problem.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

Union of Sets<\/h3>\n

Suppose that Set C has the elements {1, 2, 3, 4} and Set D has the elements {5, 6, 7, 8}.\u00a0 The union of Sets C and D (written in symbol form as C D), would consist of {1, 2, 3, 4, 5, 6, 7, 8}.\u00a0 Similar to the rules for intersection, if both sets to be combined were infinite, the rules for generating their union would need to be combined.\u00a0 Suppose that Set F were defined as {all odd integers} and Set G were defined as {all even integers}.\u00a0 Their union would be {all integers}.\u00a0 It wouldn\u2019t matter if the integers were odd or even, because the union would contain elements of both.<\/p>\n

Intersection or Union?<\/h3>\n

Suppose that the problem is one of probability.\u00a0 An unbiased die (singular of dice) has six possible outcomes when it is tossed.\u00a0 The probability of tossing an even number and a number greater than 2 is the intersection of two sets.\u00a0 If set H is {2, 4, 6} and set I is {3, 4, 5, 6}, the intersection of those sets is {4, 6}, or about a 33% probability. Suppose set J consisted of the numbers {1, 2} and set K consisted of the numbers {3, 4, 5} as faces of the unbiased die.\u00a0 The probability of tossing either of the numbers in set J or set K or {1, 2, 3, 4, 5}, a 5\/6 probability.<\/p>\n\n\n\n
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Figure 3:\u00a0 The union of sets\u00a0produces a new set that combines the contents of all the sets.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"monohybridcross\"<\/a><\/p>\n

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Overview The intersection of sets refers to the elements that both sets have in common, while the union of sets refers to the elements that both sets have together.\u00a0 If the sets are finite, the elements of the new set can be listed.\u00a0 Otherwise, they can be described graphically, algebraically, or by the rule that […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[2696,2697,2698],"class_list":["post-7035","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-intersection-of-sets","tag-union-of-sets","tag-venn-diagram"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7035","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=7035"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/7035\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=7035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=7035"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=7035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}