{"id":9519,"date":"2022-01-15T23:34:56","date_gmt":"2022-01-15T18:04:56","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9519"},"modified":"2022-01-15T23:34:59","modified_gmt":"2022-01-15T18:04:59","slug":"prove-that-empty-set-is-a-subset-of-every-set","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/prove-that-empty-set-is-a-subset-of-every-set\/","title":{"rendered":"Prove that Empty Set is a Subset of Every Set."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Let A be any set and \\(\\phi\\) be the empty set.<\/p>\n<p>In order to show that \\(\\phi\\) \\(\\subseteq\\) A, we must show that every element of \\(\\phi\\) is an element of A also. But, \\(\\phi\\) contains no element.<\/p>\n<p>So, every element of \\(\\phi\\) is in A.<\/p>\n<p>Hence, \\(\\phi\\) is the subset of A.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Let A be any set and \\(\\phi\\) be the empty set. In order to show that \\(\\phi\\) \\(\\subseteq\\) A, we must show that every element of \\(\\phi\\) is an element of A also. But, \\(\\phi\\) contains no element. So, every element of \\(\\phi\\) is in A. Hence, \\(\\phi\\) is the subset of 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":[43,56],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Prove that Empty Set is a Subset of Every Set. - Mathemerize<\/title>\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\/prove-that-empty-set-is-a-subset-of-every-set\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prove that Empty Set is a Subset of Every Set. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Let A be any set and (phi) be the empty set. 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