{"id":188844,"date":"2025-02-07T10:29:21","date_gmt":"2025-02-07T10:29:21","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=188844"},"modified":"2025-02-07T10:29:22","modified_gmt":"2025-02-07T10:29:22","slug":"prove-the-absorption-law-x-xy-x-using-the-other-laws","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/07\/prove-the-absorption-law-x-xy-x-using-the-other-laws\/","title":{"rendered":"Prove the absorption law x + xy = x using the other laws"},"content":{"rendered":"\n<p>Prove the absorption law x + xy = x using the other laws in Table 5.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-149.png\" alt=\"\" class=\"wp-image-188845\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To prove the absorption law ( x + xy = x ) using Boolean algebra, we can apply several fundamental laws. Here&#8217;s a step-by-step derivation:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Distributive Law<\/strong>: actor out ( x ) from the left-hand side: [<br>x + xy = x(1 + y)<br>]<br>his step utilizes the distributive property, which states that ( a + ab = a(1 + b) ).<\/li>\n\n\n\n<li><strong>Domination Law<\/strong>: implify ( 1 + y ) to 1: [<br>x(1 + y) = x \\times 1<br>]<br>ccording to the domination law, ( 1 + y = 1 ) for any Boolean variable ( y ).<\/li>\n\n\n\n<li><strong>Identity Law<\/strong>: implify ( x \\times 1 ) to ( x ): [<br>x \\times 1 = x<br>]<br>he identity law states that ( a \\times 1 = a ) for any Boolean variable ( a ).<br>hus, we&#8217;ve shown that ( x + xy = x ), confirming the absorption law.<br><strong>Explanation of the Laws Used<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Distributive Law<\/strong>: his law allows us to factor expressions in Boolean algebra. It states that ( a + ab = a(1 + b) ), which is analogous to factoring in regular algebra.<\/li>\n\n\n\n<li><strong>Domination Law<\/strong>: his law simplifies expressions involving the OR operation. It states that ( 1 + y = 1 ) for any Boolean variable ( y ). This is because, in Boolean logic, the OR operation with 1 always results in 1.<\/li>\n\n\n\n<li><strong>Identity Law<\/strong>: his law simplifies expressions involving the AND operation. It states that ( a \\times 1 = a ) for any Boolean variable ( a ). This is because, in Boolean logic, the AND operation with 1 leaves the other operand unchanged.<br>y applying these laws, we can simplify complex Boolean expressions and prove various identities, such as the absorption law.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Prove the absorption law x + xy = x using the other laws in Table 5. The Correct Answer and Explanation is : To prove the absorption law ( x + xy = x ) using Boolean algebra, we can apply several fundamental laws. Here&#8217;s a step-by-step derivation:<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-188844","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188844","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=188844"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/188844\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=188844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=188844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=188844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}