{"id":9513,"date":"2022-01-15T23:26:48","date_gmt":"2022-01-15T17:56:48","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9513"},"modified":"2022-01-15T23:52:22","modified_gmt":"2022-01-15T18:22:22","slug":"what-are-subsets-in-math-proper-and-improper-subsets","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-are-subsets-in-math-proper-and-improper-subsets\/","title":{"rendered":"What are Subsets in Math – Proper and Improper Subsets"},"content":{"rendered":"

Here you will learn what are subsets in math i.e. proper subsets and improper subsets with examples.<\/p>\n

Let’s begin –<\/p>\n

What are Subsets in Math ?<\/h2>\n

Definition<\/strong> : Let A and B be two sets. If every element of A is an element of B, then A is called a subset of B.<\/p>\n

If A is a subset of B, we write A \\(\\subset\\) B, which is read as “A is a subset of B” or “A is contained in B”.<\/p>\n

Thus,\u00a0 A \\(\\subseteq\\) B\u00a0 if\u00a0 a \\(\\in\\) A\u00a0 \\(\\implies\\)\u00a0 a \\(\\in\\) B.<\/p>\n

The symbol “\\(\\implies\\)” stands for “implies”.<\/p>\n

If A is a subset of B, we say that B contains A or B is a super set of A and we write B \\(\\supset\\) A.<\/p>\n

If A is not a subset of B, we write A \\(\\nsubseteq\\) B.<\/p>\n

Improper Subset<\/h2>\n

Definition<\/strong> : Every set is a subset of itself and the empty set is subset of every set. These two subsets are called improper subsets<\/strong>.<\/p>\n

Example<\/strong><\/span> : Let Set A = {1, 2, 3}. Write its improper subsets.<\/p>\n

Solution<\/span><\/strong> : Since every set is a subset of itself. Therefore {1, 2, 3} is subset of A and empty set (\\(\\phi\\)) is a subset of every set.<\/p>\n

\\(\\implies\\) {1, 2, 3} and \\(\\phi\\) are improper subsets<\/strong> of the given subset A.<\/p>\n

Proper Subset<\/h2>\n

Definition\u00a0<\/strong>: A subset A of a set B is called a proper subset<\/strong> of B if A \\(\\ne\\) B and we write A \\(\\subset\\) B. In such a case we also say that B is a super set of A.<\/p>\n

Thus, if A is a proper subset of B, then there exist an element x \\(\\in\\) B such that x \\(\\notin\\) A.<\/p>\n

In the example given below set B is the proper subset<\/strong> of set A.<\/p>\n

Example<\/strong><\/span> : Let Set A = {1, 2, 3}, Set B = {1} and Set C = {1, 4}.<\/p>\n

Then {1} \\(\\subseteq\\) {1, 2, 3} but {1, 4} \\(\\nsubseteq\\) {1, 2, 3}<\/p>\n

\\(\\implies\\) Set B is the subset of A because every element of B is in Set A. But Set C is not the subset of A because element 4 is not in Set A.<\/p>\n

Theorems on Subsets<\/h2>\n

(i) Every set is a subset of itself.<\/p>\n

(ii) The empty set is a subset of every set.<\/a><\/p>\n

(iii) The total number of subsets of a finite set containing n elements is \\(2^n\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what are subsets in math i.e. proper subsets and improper subsets with examples. Let’s begin – What are Subsets in Math ? Definition : Let A and B be two sets. If every element of A is an element of B, then A is called a subset of B. If A …<\/p>\n

What are Subsets in Math – Proper and Improper Subsets<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[16],"tags":[751,750,749],"yoast_head":"\nWhat are Subsets in Math - Proper and Improper Subsets<\/title>\n<meta name=\"description\" content=\"In this post you will learn what are subsets in math i.e. proper and improper subsets with examples and its theorems.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/what-are-subsets-in-math-proper-and-improper-subsets\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What are Subsets in Math - 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