{"id":3037,"date":"2012-08-09T15:09:08","date_gmt":"2012-08-09T15:09:08","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=3037"},"modified":"2014-12-02T08:32:06","modified_gmt":"2014-12-02T08:32:06","slug":"schooltutoring-com-reviews-algebra-numerical-relations","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/schooltutoring-com-reviews-algebra-numerical-relations\/","title":{"rendered":"SchoolTutoring Reviews Algebra – Numerical Relations"},"content":{"rendered":"

Let A <\/strong>and B<\/strong> be two non-empty sets. Then the relation which is usually denoted by R <\/strong>from A to B <\/strong>is defined as the set of ordered pairs (in each of which the first element is from A<\/strong> and the second element is from B)<\/strong> satisfying a certain condition.<\/p>\n

The set of all first elements\u00a0 of ordered pairs of R is called \u201cDomain\u201d of R.<\/strong><\/p>\n

The set of all second elements of ordered pairs is called \u201crange\u201d of R.
\n<\/strong><\/p>\n

Example:<\/em><\/strong><\/p>\n

If A = {1,4,6}, B= {1, 2, 3}<\/strong> then construct a relation R <\/strong>from A to B <\/strong>describing \u201cis a multiple of\u201d.<\/p>\n

\u00a0<\/strong>Since 1<\/strong> \u201cis amultiple of\u201d 1, (1,1)<\/strong> is in R<\/strong>.<\/p>\n

Since 4 <\/strong>\u201cis a multiple of\u201d 2 (4,2)<\/strong> is in R.
\n<\/strong><\/p>\n

Similarly we can find all the ordered pairs of R.
\n<\/strong><\/p>\n

Hence R = {(1,1)(4,1)(4,2)(6,1)(6,2)(6,3)}
\n<\/strong><\/p>\n

Here, Domain of R = {1,4,6}<\/strong> and<\/p>\n

Range of R = {1,2,3}
\n<\/strong><\/p>\n

Note : <\/strong>Though (4,3)<\/strong> is an ordered pair, it won\u2019t be there in R <\/strong>because 4 <\/strong>is not a multiple of 3.
\n<\/strong><\/p>\n

<\/strong>Graphical representation of a relation:<\/h4>\n

A relation is graphically represented\u00a0 as follows.<\/p>\n

If A = {1,4,6}, B= {1, 2, 3}<\/strong> then a relation R = {(1,1)(4,2)(6,2)(6,3)} <\/strong>from A<\/strong> to B<\/strong> is represented through a graph as follows.<\/p>\n

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

Types of relations:<\/h4>\n

The types of relations are nothing but their properties. There are different types of relations namely reflexive, symmetric, transitive and anti symmetric<\/strong> which are defined and explained as follows through real life examples.<\/p>\n

Reflexive relation:<\/strong><\/h5>\n

A relation R<\/em> is said to be reflexive over a set A<\/em> if (a,a) \u20ac R<\/em> for every a<\/em> \u20ac R<\/em>.<\/p>\n

Example:<\/strong><\/em><\/p>\n

If A is the set of all males in a family, then the relation \u201cis brother of\u201d is not reflexive over A. Because any person from the set A cannot be brother of himself.<\/p>\n

Symmetric relation:<\/strong><\/h5>\n

A relation R<\/em> is said to be symmetric if (a,b) \u20ac R => (b,a) \u20ac R<\/p>\n

Example:<\/strong><\/em><\/p>\n

If A is the set of all males in a family, then the relation \u201cis brother of\u201d is symmetric over A.<\/p>\n

Because if a<\/em> is brother of b<\/em> then b <\/em>is brother of a<\/em>.<\/p>\n

Transitive relation:<\/strong><\/h5>\n

A relation R<\/em> is said to be symmetric if (a, b) \u20ac R, (b, c) \u20ac R => (a, c) \u20ac R.<\/p>\n

Example:<\/strong><\/em><\/p>\n

If A is the set of all males in a family, then the relation \u201cis brother of\u201d is transitive over A.<\/p>\n

Because if a<\/em> is brother of b<\/em> and b <\/em>is brother of c<\/em> then a<\/em> is brother of c<\/em>.<\/p>\n

Anti symmetric relation:<\/h5>\n

A relation R<\/em> is said to be anti symmetric if (a,b) \u20ac R and (b, a) \u20ac R => a=b.<\/p>\n

Example:<\/strong><\/em><\/p>\n

The relation \u201c\u2264\u201d on the set of real numbers is anti symmetric because if a \u2264 b and b \u2264 a then a=b.<\/p>\n

 <\/p>\n

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Oxnard visit: Tutoring in Oxnard. <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Let A and B be two non-empty sets. Then the relation which is usually denoted by R from A to B is defined as the set of ordered pairs (in each of which the first element is from A and the second element is from B) satisfying a certain condition. The set of all first […]<\/p>\n","protected":false},"author":19,"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":[784,841,1331,2047,2063,2178,2182,2183],"class_list":["post-3037","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-how-are-ordered-pairs-used","tag-how-do-yo-ufind-relations","tag-picture-of-relations","tag-what-are-ordered-pairs","tag-what-are-relations","tag-what-is-a-reflexive-relation","tag-what-is-a-symmetric-relation","tag-what-is-a-transitive-relation"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3037","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=3037"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/3037\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=3037"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=3037"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=3037"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}