{"id":3663,"date":"2021-08-05T23:45:20","date_gmt":"2021-08-05T23:45:20","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3663"},"modified":"2022-01-20T17:47:02","modified_gmt":"2022-01-20T12:17:02","slug":"types-of-relations-in-math","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/types-of-relations-in-math\/","title":{"rendered":"Types of Relations in Math"},"content":{"rendered":"

In this post, we will learn various types of relations in math on a set.<\/p>\n

Let’s begin-<\/p>\n

Types of Relations in Math<\/h2>\n

1). Void, Universal and Identity Relation<\/h2>\n

Void Relation : <\/strong>Let A be a set. Then \\(\\phi\\) \\(\\subseteq\\) A \\(\\times\\) A and so it is a relation on A. This relation is called  the void or empty relation on set A.<\/p>\n

In other words, a relation R on the set A is called void or empty relation, if no element of A is related to any element of A.<\/p>\n

for example<\/span> : Consider the relation R on set A = {1,2,3,4,5} defined by R = {(a,b) : a-b = 12}.<\/p>\n

Universal Relation : <\/strong>Let A be a set. Then, A \\(\\times\\) A \\(\\subseteq\\) A \\(\\times\\) A and so it is a relation on A. This relation is called universal relation on A.<\/p>\n

for example<\/span> : Consider the relation R on set A = {1,2,3,4,5,6} defined by R = {(a,b) : |a-b| \\(\\ge\\) 0}.<\/p>\n

Identity Relation : <\/strong>Let A be a set. Then, the relation \\(I_A\\) = {(a, a) : a \\(\\in\\) A} on A is called the identity relation on A.<\/p>\n

In other words, a relation \\(I_A\\) on A is called the identity relation if every element of A is related to itself only.<\/p>\n

for example : If A = {1,2,3}, then the relation \\(I_A\\) = {(1,1),(2,2),(3,3)} is the identity relation on set A.<\/p>\n

2). Reflexive Relation<\/h2>\n

A relation R on a set A is said to be reflexive if every element of A is related to itself.<\/p>\n

\n

Thus, R is reflexive \\(\\implies\\) (a, a) \\(\\in\\) R for all a \\(\\in\\) R<\/p>\n<\/blockquote>\n

for example<\/span> : If A = {1,2,3}, then the relation R = {(1,1),(2,2),(3,3),(1,3),(2,1)} is the reflexive relation on A, But \\(R_1\\) = {(1,1),(3,3),(3,2),(2,1)}  is not a reflexive relation on A, because 2 \\(\\in\\) A but (2,2) \\(\\notin\\) \\(R_1\\).<\/p>\n

3). Symmetric Relation<\/h2>\n

A relation R on a set A is said to be symmetric iff<\/p>\n

\n

(a,b) \\(\\in\\) R \\(\\implies\\) (b,a) \\(\\in\\) R for all a,b \\(\\in\\) A<\/p>\n

i.e. aRb \\(\\implies\\) bRa for all a, b \\(\\in\\) A.<\/p>\n<\/blockquote>\n

for example<\/span> : If A = {1,2,3,4}, then the relation R = {(1,3),(1,4),(3,1),(2,2),(4,1)} is the symmetric relation on A, But \\(R_1\\) = {(1,1),(3,3),(2,2),(1,3)}  is not a symmetric relation on A, because (1,3) \\(\\in\\) \\(R_1\\) but (3,1) \\(\\notin\\) \\(R_1\\).<\/p>\n

4). Transitive Relation<\/h2>\n

Let A be any set. A relation R on A is said to be transitive relation iff<\/p>\n

\n

(a,b) \\(\\in\\) R and (b,c) \\(\\in\\) R \\(\\implies\\) (a,c) \\(\\in\\) R for all a, b, c \\(\\in\\) A.<\/p>\n

i.e. aRb and bRc  \\(\\implies\\) aRc for all a,b,c \\(\\in\\) A.<\/p>\n<\/blockquote>\n

for example<\/span> : If A = {1,2,3}, then the relation R = {(1,2),(2,3),(1,3),(2,2)} is the transitive relation on A, But \\(R_1\\) = {(1,2),(2,3),(2,2),(1,1)}  is not a transitive relation on A, because (1,3) and (2,3) \\(\\in\\) \\(R_1\\) but (1,3) \\(\\notin\\) \\(R_1\\).<\/p>\n

5). Equivalence Relation<\/h2>\n
\n

A relation R on a set A is said to be an equivalence relation on A if it is reflexive, symmetric and transitive.<\/p>\n<\/blockquote>\n

for example<\/span> : If A = {1,2,3}, then the relation R = {(1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(1,3).(3,2),(3,1)} is the equivalence relation on A, because {(1,1),(2,2),(3,3)} \\(\\in\\) R hence it is reflexive, {(2,1),(1,2),(2,3),(3,2),(1,3),(3,1)} \\(\\in\\) R  hence it is symmetric on A, {(1,2),(2,3),(1,3)} and {(1,3),(3,2),(1,2)} \\(\\in\\) R hence it is transitive.<\/p>\n

Therefore, it is a equivalence relation.<\/p>\n

Hope you learnt types of relations in math, learn more concepts of relations and practice more questions to get ahead in the competition. Good luck!<\/p>\n\n\n

\n
Next – What is Inverse Relation \u2013 Definition & Example<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – What is Cartesian Product of Sets<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

In this post, we will learn various types of relations in math on a set. Let’s begin- Types of Relations in Math 1). Void, Universal and Identity Relation Void Relation : Let A be a set. Then \\(\\phi\\) \\(\\subseteq\\) A \\(\\times\\) A and so it is a relation on A. This relation is called  the void …<\/p>\n

Types of Relations in Math<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[17],"tags":[582,579,580,581,578],"yoast_head":"\nTypes of Relations in Math - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn what are the types of relations in math i.e. reflexive, symmetric, transitive and equivalence relation.\" \/>\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\/types-of-relations-in-math\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Types of Relations in Math - 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