{"id":4448,"date":"2025-03-08T12:51:01","date_gmt":"2025-03-08T07:21:01","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=4448"},"modified":"2025-07-16T14:18:32","modified_gmt":"2025-07-16T08:48:32","slug":"laws-of-boolean-algebra","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/boolean-algebra\/laws-of-boolean-algebra","title":{"rendered":"Laws of Boolean Algebra"},"content":{"rendered":"<p>The Boolean algebra is governed by certain well developed rules and laws.<\/p>\n<h2>Commutative Lawswell-developed<\/h2>\n<ul>\n<li>The commutative law allows change in position of AND or OR variables. There are two commutative laws.<br \/>\n(i) A + B = B + A<br \/>\nThus, the order in which the variables are ORed is immaterial.<br \/>\n(ii) A \u22c5 B = B \u22c5 A<br \/>\nThus, the order in which the variables are ANDed is immaterial.<\/li>\n<li>This law can be extended to any number of variables.<\/li>\n<\/ul>\n<h2>Associative Laws<\/h2>\n<ul>\n<li>The associative law allows grouping of variables. There are two associative laws<br \/>\n(i) (A + B) + C = A + (B + C)<br \/>\nThus, the way the variables are grouped and ORed is immaterial.<br \/>\n(ii) (A \u22c5 B) \u22c5 C = A \u22c5 (B \u22c5 C)<br \/>\nThus, the way the variables are grouped and ANDed is immaterial.<\/li>\n<li>This law can be extended to any number of variables.<\/li>\n<\/ul>\n<h3>Distributive Laws<\/h3>\n<ul>\n<li>The distributive law allows factoring or multiplying out of expressions. There are two distributive<br \/>\nlaws.<br \/>\n(i) A(B + C) = AB + AC<br \/>\n(ii) A + BC = (A + B) (A + C)<\/li>\n<li>This law is applicable for single variable as well as a combination of variables.<\/li>\n<\/ul>\n<h3>Idempotent Laws<\/h3>\n<ul>\n<li>Idempotent means the same value. There are two Idempotent laws<br \/>\n(i) A \u22c5 A = A<br \/>\ni.e., ANDing of a variable with itself is equal to that variable only.<br \/>\n(ii) A + A = A<br \/>\ni.e., ORing of a variable with itself is equal to that variable only.<\/li>\n<\/ul>\n<h3>Absorption Laws<\/h3>\n<ul>\n<li>There are two absorption laws<br \/>\n(i) A + AB = A(1 + B) = A (ii)A (A + B) = A<\/li>\n<\/ul>\n<h3>Involutory Law<\/h3>\n<ul>\n<li>This law states that, for any variable \u2018A\u2019<br \/>\nA = (A\u2032)\u2032 = A<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ee\/boolean-algebra\/8085-microprocessor\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ee\/boolean-algebra\/boolean-algebraic-theorem\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-boolean-algebra\" target=\"_blank\" rel=\"noopener\"><strong>What is Boolean algebra?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Boolean algebra is governed by certain well developed rules and laws. Commutative Lawswell-developed The commutative law allows change in<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1291,5],"tags":[1293,1430,1428,1292,1427,1295,1426,1294,1425,1429],"class_list":["post-4448","post","type-post","status-publish","format-standard","hentry","category-boolean-algebra","category-ee","tag-absorption-laws","tag-boolean-digital-logic","tag-boolean-expressions","tag-commutative-laws","tag-digital-circuits","tag-distributive-laws","tag-electrical-engineering-logic","tag-involutory-law","tag-laws-of-boolean-algebra","tag-logic-laws"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4448","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=4448"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4448\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=4448"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=4448"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=4448"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}