{"id":89960,"date":"2025-06-01T10:17:59","date_gmt":"2025-06-01T10:17:59","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89960"},"modified":"2025-06-01T10:17:59","modified_gmt":"2025-06-01T10:17:59","slug":"the-next-three-03-items-have-two-premises-and-two-conclusions-if-th","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/","title":{"rendered":"The next three (03) items have two premises and two conclusions. If th"},"content":{"rendered":"<p>The next three (03) items have two premises and two conclusions. If the premises are assumed to be true (irrespective of factuality), then, in respect of each of the items given below, which of the following conclusions follow logically ?<br \/>\nPremises: All metals are grey in colour. Some metals are heavy.<br \/>\nConclusions:<\/p>\n<ul>\n<li>I. All heavy metals are grey in colour.<\/li>\n<li>II. All light metals are not grey in colour.<\/li>\n<\/ul>\n<p>[amp_mcq option1=&#8221;Only I&#8221; option2=&#8221;Only II&#8221; option3=&#8221;Both I and II&#8221; option4=&#8221;Neither I nor II&#8221; correct=&#8221;option1&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC CAPF &#8211; 2015<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-capf-2015.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-capf-2015\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nOnly Conclusion I follows logically from the given premises.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\nPremise 1: All metals are grey in colour. (M \u2286 G)<br \/>\nPremise 2: Some metals are heavy. (Some M are H)<br \/>\nConclusion I: All heavy metals are grey in colour.<br \/>\n&#8220;Heavy metals&#8221; refers to the set of things that are both heavy and metal (H \u2229 M). According to Premise 1, anything that is a metal is grey (M \u2286 G). Therefore, if something is a heavy metal, it must first be a metal, and thus it must be grey. So, H \u2229 M \u2286 G. Conclusion I logically follows.<br \/>\nConclusion II: All light metals are not grey in colour.<br \/>\n&#8220;Light metals&#8221; refers to the set of things that are metals but not heavy (M \u2229 not-H). According to Premise 1, all metals are grey (M \u2286 G). This means *any* metal, regardless of whether it is heavy or light, must be grey. Therefore, light metals are grey. Conclusion II, stating that light metals are *not* grey, contradicts Premise 1 and is false.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nThis is a standard problem involving categorical syllogisms. Using Venn diagrams can also help visualize the relationships. Draw three overlapping circles for Metals (M), Grey (G), and Heavy (H). Premise 1 (All M are G) means the part of M outside G is empty. Premise 2 (Some M are H) means there is at least one element in the intersection of M and H. Conclusion I (All H\u2229M are G) means the part of (H\u2229M) outside G is empty, which is true because M is entirely within G. Conclusion II (All M\u2229not-H are not-G) means the part of (M\u2229not-H) inside G is empty, which is false because M is entirely within G, meaning M\u2229not-H must also be within G.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>The next three (03) items have two premises and two conclusions. If the premises are assumed to be true (irrespective of factuality), then, in respect of each of the items given below, which of the following conclusions follow logically ? Premises: All metals are grey in colour. Some metals are heavy. Conclusions: I. All heavy &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"The next three (03) items have two premises and two conclusions. If th\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/#more-89960\">Detailed Solution<span class=\"screen-reader-text\">The next three (03) items have two premises and two conclusions. If th<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1443,1102],"class_list":["post-89960","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1443","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The next three (03) items have two premises and two conclusions. If th<\/title>\n<meta name=\"description\" content=\"Only Conclusion I follows logically from the given premises. Premise 1: All metals are grey in colour. (M \u2286 G) Premise 2: Some metals are heavy. (Some M are H) Conclusion I: All heavy metals are grey in colour. &quot;Heavy metals&quot; refers to the set of things that are both heavy and metal (H \u2229 M). According to Premise 1, anything that is a metal is grey (M \u2286 G). Therefore, if something is a heavy metal, it must first be a metal, and thus it must be grey. So, H \u2229 M \u2286 G. Conclusion I logically follows. Conclusion II: All light metals are not grey in colour. &quot;Light metals&quot; refers to the set of things that are metals but not heavy (M \u2229 not-H). According to Premise 1, all metals are grey (M \u2286 G). This means *any* metal, regardless of whether it is heavy or light, must be grey. Therefore, light metals are grey. Conclusion II, stating that light metals are *not* grey, contradicts Premise 1 and is false.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The next three (03) items have two premises and two conclusions. If th\" \/>\n<meta property=\"og:description\" content=\"Only Conclusion I follows logically from the given premises. Premise 1: All metals are grey in colour. (M \u2286 G) Premise 2: Some metals are heavy. (Some M are H) Conclusion I: All heavy metals are grey in colour. &quot;Heavy metals&quot; refers to the set of things that are both heavy and metal (H \u2229 M). According to Premise 1, anything that is a metal is grey (M \u2286 G). Therefore, if something is a heavy metal, it must first be a metal, and thus it must be grey. So, H \u2229 M \u2286 G. Conclusion I logically follows. Conclusion II: All light metals are not grey in colour. &quot;Light metals&quot; refers to the set of things that are metals but not heavy (M \u2229 not-H). According to Premise 1, all metals are grey (M \u2286 G). This means *any* metal, regardless of whether it is heavy or light, must be grey. Therefore, light metals are grey. Conclusion II, stating that light metals are *not* grey, contradicts Premise 1 and is false.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:17:59+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The next three (03) items have two premises and two conclusions. If th","description":"Only Conclusion I follows logically from the given premises. Premise 1: All metals are grey in colour. (M \u2286 G) Premise 2: Some metals are heavy. (Some M are H) Conclusion I: All heavy metals are grey in colour. \"Heavy metals\" refers to the set of things that are both heavy and metal (H \u2229 M). According to Premise 1, anything that is a metal is grey (M \u2286 G). Therefore, if something is a heavy metal, it must first be a metal, and thus it must be grey. So, H \u2229 M \u2286 G. Conclusion I logically follows. Conclusion II: All light metals are not grey in colour. \"Light metals\" refers to the set of things that are metals but not heavy (M \u2229 not-H). According to Premise 1, all metals are grey (M \u2286 G). This means *any* metal, regardless of whether it is heavy or light, must be grey. Therefore, light metals are grey. Conclusion II, stating that light metals are *not* grey, contradicts Premise 1 and is false.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/","og_locale":"en_US","og_type":"article","og_title":"The next three (03) items have two premises and two conclusions. If th","og_description":"Only Conclusion I follows logically from the given premises. Premise 1: All metals are grey in colour. (M \u2286 G) Premise 2: Some metals are heavy. (Some M are H) Conclusion I: All heavy metals are grey in colour. \"Heavy metals\" refers to the set of things that are both heavy and metal (H \u2229 M). According to Premise 1, anything that is a metal is grey (M \u2286 G). Therefore, if something is a heavy metal, it must first be a metal, and thus it must be grey. So, H \u2229 M \u2286 G. Conclusion I logically follows. Conclusion II: All light metals are not grey in colour. \"Light metals\" refers to the set of things that are metals but not heavy (M \u2229 not-H). According to Premise 1, all metals are grey (M \u2286 G). This means *any* metal, regardless of whether it is heavy or light, must be grey. Therefore, light metals are grey. Conclusion II, stating that light metals are *not* grey, contradicts Premise 1 and is false.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:17:59+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/","name":"The next three (03) items have two premises and two conclusions. If th","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:17:59+00:00","dateModified":"2025-06-01T10:17:59+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Only Conclusion I follows logically from the given premises. Premise 1: All metals are grey in colour. (M \u2286 G) Premise 2: Some metals are heavy. (Some M are H) Conclusion I: All heavy metals are grey in colour. \"Heavy metals\" refers to the set of things that are both heavy and metal (H \u2229 M). According to Premise 1, anything that is a metal is grey (M \u2286 G). Therefore, if something is a heavy metal, it must first be a metal, and thus it must be grey. So, H \u2229 M \u2286 G. Conclusion I logically follows. Conclusion II: All light metals are not grey in colour. \"Light metals\" refers to the set of things that are metals but not heavy (M \u2229 not-H). According to Premise 1, all metals are grey (M \u2286 G). This means *any* metal, regardless of whether it is heavy or light, must be grey. Therefore, light metals are grey. Conclusion II, stating that light metals are *not* grey, contradicts Premise 1 and is false.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-next-three-03-items-have-two-premises-and-two-conclusions-if-th\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"The next three (03) items have two premises and two conclusions. 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