Subsets of a Given Set mean the subset having the elements present in a set. In other words, Subsets are a part of the set. A set is nothing but a collection of elements placed within curly braces. The example of a set is {a, b, c}. If we take a set of even numbers and name it as A and set B has {2, 4, 6}, then B is the subset of set A. It is represented as B\u2286A. The elements of sets may be variables, groups of real numbers, constants, or whole numbers, etc.<\/p>\n
The subset is said to be a part of the set. Subset must have the elements that present in a set. If set A is said to be a subset of Set B, then all the elements of Set A are must present in Set B. Set A is contained inside Set B.
\nExample: If Set A has {C, D} and set B has {C, D, E}, then A is the subset of B because all the elements of A are also present in set B. The subset is denoted by the symbol \u2286 we read as ‘subset of’. A \u2286 B; which means Set A is a subset of Set B.<\/p>\n
The subset of any given set must consist of all possible sets along with the elements and also having a null set. Check out the below example to understand the subset of a set.
\nExample: A = {7, 6, 8, 9}
\nSolution: Given that A = {6, 7, 8, 9}.
\nSubsets = {}, {6}, {7}, {8}, {9},
\n{6,7}, {6,8}, {6,9}, {7,8},{7,9}, {8,9},
\n{6,7,8}, {7,8,9}, {6,8,9}, {6,7,9}
\n{6, 7, 8, 9}<\/p>\n
Mainly, there are two different types of subsets available. they are classified as<\/p>\n
The proper subset contains some elements of an original set along with a null set. Set A is treated to be a proper subset of Set B if Set B has at least one element that is not present in Set A. A proper subset is denoted by \u2282 and it is read as \u2018is a proper subset of\u2019. We can show a proper subset for set A and set B as A \u2282 B.<\/p>\n
If we take n number of elements from a set having N number of elements, then it shows as \u00a0N<\/sup>Cn<\/sub> number of ways. The number of possible subsets having n number of elements from a set containing N number of elements is equal to \u00a0N<\/sup>Cn<\/sub>.<\/p>\n Also, Read:<\/p>\n A subset that has all elements of the original set is called an improper subset. It is denoted by \u2286. The Improper Subset consists of all elements of a set that doesn’t miss any element.<\/p>\n Example: Set P = {3, 5, 7} Note: The empty set is an improper subset of itself but it is a proper subset of any other set.<\/p>\n The power set is defined as the collection of all the subsets. It is represented by P(A). Let us consider a set that consists of n elements, then the number of a subset of the given set is 2n <\/sup>and the number of proper subsets of the given subset is given by 2n<\/sup>-1.<\/p>\n Example: If set A consists the elements, A = {c, d}, then the proper subset of the given subset are {}, {c}, {d}. The below are some of the important properties of subsets.<\/p>\n 1. If A {2, 3, 7}, then write all the possible subsets of A. Find their numbers?<\/p>\n Solution: Number of proper subsets are 7 = 8 – 1 = 2\u00b3 – 1.<\/p>\n 2. If the number of elements in a set is 4, find the number of subsets and proper subsets.<\/p>\n Solution: 3. If A = {5, 6, 7, 8, 9}<\/p>\n The formula to calculate the number of proper subsets of a given set is 2n<\/sup>\u00a0\u2013 1 Subsets of a Given Set mean the subset having the elements present in a set. In other words, Subsets are a part of the set. A set is nothing but a collection of elements placed within curly braces. The example of a set is {a, b, c}. If we take a set of even numbers … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":60756,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Subsets-of-a-Given-Set.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/60754"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=60754"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/60754\/revisions"}],"predecessor-version":[{"id":138120,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/60754\/revisions\/138120"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/60756"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=60754"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=60754"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=60754"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Improper Subset<\/h4>\n
\nThe subsets of P are {}, {3}, {5}, {7}, {3,5}, {5,7}, {3,7} and {3,5,7}.
\nWhere, {}, {3}, {5}, {7}, {3,5}, {5,7}, {3,7} are the proper subsets and {3,5,7} is the improper subsets. Therefore, we can write {3,5,7} \u2286 P.<\/p>\nPower Set<\/h4>\n
\nIf A is set having elements {a, b}. Then the power set of A will be
\nP(A) =\u00a0 {\u2205,\u00a0{a}, {b}, {a, b}}<\/p>\nHow many Subsets and Proper Subsets does a Set have?<\/h3>\n
\nThe number of elements in the set is 2.
\nThe formula to find the number of proper subsets is 2n<\/sup> \u2013 1.
\n= 2\u00b2 \u2013 1
\n= 4 \u2013 1
\n= 3
\nThus, the number of proper subset for the given set is 3 ({ }, {c}, {d}).<\/p>\nProperties of Subsets<\/h3>\n
\n
Solved Examples on Subsets of a Given Set<\/h3>\n
\nGiven that set A {2, 3, 7}.
\nLet us write all the possible subsets of a given set.
\nThe subset of A containing no elements – {\u00a0 }
\nThe subset of A containing one element each – {2} {3} {7}
\nThe subset of A containing two elements each – {2, 3} {2, 7} {3, 7}
\nThe subset of A containing three elements – {2, 3, 7}
\nTherefore, all possible subsets of A are { }, {2}, {3}, {7}, {2, 3}, {2, 7}, {3, 7}, {2, 3, 7}
\nTherefore, the number of all possible subsets of A is 8 which is equal to 2\u00b3.
\nProper subsets are = {\u00a0 }, {2}, {3}, {7}, {2, 3}, {3, 7}<\/p>\n
\nNumber of elements in a set = 4
\nThen, number of subsets = 24<\/sup> = 16
\nAlso, the number of proper subsets = 24<\/sup> – 1
\n= 16 \u2013 1 = 15<\/p>\n
\nthen the number of proper subsets = 25<\/sup> \u2013 1
\n= 32 – 1 = 31\u00a0\u00a0 {Take [ 2n<\/sup> \u2013 1]}
\nand the formula to calculate the number of subsets of a given set is 2n<\/sup>
\npower set of A = 25<\/sup> = 32 {Take [2n<\/sup>]}<\/p>\n","protected":false},"excerpt":{"rendered":"