{"id":89222,"date":"2025-06-01T09:59:17","date_gmt":"2025-06-01T09:59:17","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89222"},"modified":"2025-06-01T09:59:17","modified_gmt":"2025-06-01T09:59:17","slug":"consider-the-following-statements-every-square-is-a-rectangle-eve","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-statements-every-square-is-a-rectangle-eve\/","title":{"rendered":"Consider the following statements:\n  Every square is a rectangle.  Eve"},"content":{"rendered":"<p>Consider the following statements:<\/p>\n<ul>\n<li>Every square is a rectangle.<\/li>\n<li>Every rectangle is a parallelogram.<\/li>\n<li>Every parallelogram is not necessarily a square.<\/li>\n<\/ul>\n<p>Which one of the following conclusions can be drawn on the basis of the above statements ?<\/p>\n<p>[amp_mcq option1=&#8221;All parallelograms are either squares or rectangles.&#8221; option2=&#8221;A non-parallelogram figures cannot be either a square or a rectangle.&#8221; option3=&#8221;All rectangles are either squares or parallelograms.&#8221; option4=&#8221;Squares and rectangles are the only parallelograms.&#8221; correct=&#8221;option2&#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; 2009<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-capf-2009.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-capf-2009\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nThe correct option is B) A non-parallelogram figures cannot be either a square or a rectangle.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\nLet the statements be:<br \/>\n1. Every square is a rectangle. (Square -> Rectangle)<br \/>\n2. Every rectangle is a parallelogram. (Rectangle -> Parallelogram)<br \/>\n3. Every parallelogram is not necessarily a square. (Parallelogram -\/> Square)<\/p>\n<p>From statement 1 and 2, we can form a chain: Square -> Rectangle -> Parallelogram.<br \/>\nThis implies that every square is a parallelogram.<\/p>\n<p>Now let&#8217;s analyze the conclusions:<br \/>\nA) All parallelograms are either squares or rectangles. This is false. A rhombus is a parallelogram but is not necessarily a square or a rectangle.<br \/>\nB) A non-parallelogram figures cannot be either a square or a rectangle. This is true.<br \/>\nFrom Rectangle -> Parallelogram, the contrapositive is (Not Parallelogram) -> (Not Rectangle).<br \/>\nFrom Square -> Rectangle, the contrapositive is (Not Rectangle) -> (Not Square).<br \/>\nCombining these, if a figure is not a parallelogram, then it is not a rectangle. If it is not a rectangle, then it is not a square. Therefore, if a figure is a non-parallelogram, it cannot be a rectangle, and thus cannot be a square. This conclusion is logically derived from the first two statements.<br \/>\nC) All rectangles are either squares or parallelograms. This statement is technically true because all rectangles *are* parallelograms (Statement 2), and the set of squares is a subset of rectangles. So, a rectangle is always in the set of parallelograms, and sometimes in the set of squares. However, the wording &#8220;either&#8230;or&#8221; often implies mutual exclusion or at least that being a parallelogram is not always the case for a rectangle, which contradicts statement 2. Conclusion B is a more direct and stronger inference from the combined statements.<br \/>\nD) Squares and rectangles are the only parallelograms. This is false. Rhombuses and other non-rectangular parallelograms exist.<\/p>\n<p>Conclusion B is the only valid and direct conclusion that can be drawn based on the transitive property implied by the statements.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nThis question tests understanding of the hierarchy of quadrilaterals. The relationships are: Square \u2282 Rhombus, Square \u2282 Rectangle, Rhombus \u2282 Parallelogram, Rectangle \u2282 Parallelogram. Square is the most specific type, being a rectangle with equal sides, and a rhombus with right angles. Parallelogram is a broader category.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>Consider the following statements: Every square is a rectangle. Every rectangle is a parallelogram. Every parallelogram is not necessarily a square. Which one of the following conclusions can be drawn on the basis of the above statements ? [amp_mcq option1=&#8221;All parallelograms are either squares or rectangles.&#8221; option2=&#8221;A non-parallelogram figures cannot be either a square or &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"Consider the following statements:\n  Every square is a rectangle.  Eve\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-statements-every-square-is-a-rectangle-eve\/#more-89222\">Detailed Solution<span class=\"screen-reader-text\">Consider the following statements:<br \/>\n  Every square is a rectangle.  Eve<\/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":[1462,1102],"class_list":["post-89222","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1462","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>Consider the following statements:  Every square is a rectangle. Eve<\/title>\n<meta name=\"description\" content=\"The correct option is B) A non-parallelogram figures cannot be either a square or a rectangle. Let the statements be: 1. Every square is a rectangle. (Square -&gt; Rectangle) 2. Every rectangle is a parallelogram. (Rectangle -&gt; Parallelogram) 3. Every parallelogram is not necessarily a square. (Parallelogram -\/&gt; Square) From statement 1 and 2, we can form a chain: Square -&gt; Rectangle -&gt; Parallelogram. This implies that every square is a parallelogram. Now let&#039;s analyze the conclusions: A) All parallelograms are either squares or rectangles. This is false. A rhombus is a parallelogram but is not necessarily a square or a rectangle. B) A non-parallelogram figures cannot be either a square or a rectangle. This is true. From Rectangle -&gt; Parallelogram, the contrapositive is (Not Parallelogram) -&gt; (Not Rectangle). From Square -&gt; Rectangle, the contrapositive is (Not Rectangle) -&gt; (Not Square). Combining these, if a figure is not a parallelogram, then it is not a rectangle. If it is not a rectangle, then it is not a square. Therefore, if a figure is a non-parallelogram, it cannot be a rectangle, and thus cannot be a square. This conclusion is logically derived from the first two statements. C) All rectangles are either squares or parallelograms. This statement is technically true because all rectangles *are* parallelograms (Statement 2), and the set of squares is a subset of rectangles. So, a rectangle is always in the set of parallelograms, and sometimes in the set of squares. However, the wording &quot;either...or&quot; often implies mutual exclusion or at least that being a parallelogram is not always the case for a rectangle, which contradicts statement 2. Conclusion B is a more direct and stronger inference from the combined statements. D) Squares and rectangles are the only parallelograms. This is false. Rhombuses and other non-rectangular parallelograms exist. Conclusion B is the only valid and direct conclusion that can be drawn based on the transitive property implied by the statements.\" \/>\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\/consider-the-following-statements-every-square-is-a-rectangle-eve\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Consider the following statements:  Every square is a rectangle. Eve\" \/>\n<meta property=\"og:description\" content=\"The correct option is B) A non-parallelogram figures cannot be either a square or a rectangle. Let the statements be: 1. Every square is a rectangle. (Square -&gt; Rectangle) 2. Every rectangle is a parallelogram. (Rectangle -&gt; Parallelogram) 3. Every parallelogram is not necessarily a square. (Parallelogram -\/&gt; Square) From statement 1 and 2, we can form a chain: Square -&gt; Rectangle -&gt; Parallelogram. This implies that every square is a parallelogram. Now let&#039;s analyze the conclusions: A) All parallelograms are either squares or rectangles. This is false. A rhombus is a parallelogram but is not necessarily a square or a rectangle. B) A non-parallelogram figures cannot be either a square or a rectangle. This is true. From Rectangle -&gt; Parallelogram, the contrapositive is (Not Parallelogram) -&gt; (Not Rectangle). From Square -&gt; Rectangle, the contrapositive is (Not Rectangle) -&gt; (Not Square). Combining these, if a figure is not a parallelogram, then it is not a rectangle. If it is not a rectangle, then it is not a square. Therefore, if a figure is a non-parallelogram, it cannot be a rectangle, and thus cannot be a square. This conclusion is logically derived from the first two statements. C) All rectangles are either squares or parallelograms. This statement is technically true because all rectangles *are* parallelograms (Statement 2), and the set of squares is a subset of rectangles. So, a rectangle is always in the set of parallelograms, and sometimes in the set of squares. However, the wording &quot;either...or&quot; often implies mutual exclusion or at least that being a parallelogram is not always the case for a rectangle, which contradicts statement 2. Conclusion B is a more direct and stronger inference from the combined statements. D) Squares and rectangles are the only parallelograms. This is false. Rhombuses and other non-rectangular parallelograms exist. Conclusion B is the only valid and direct conclusion that can be drawn based on the transitive property implied by the statements.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-statements-every-square-is-a-rectangle-eve\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T09:59:17+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":"Consider the following statements:  Every square is a rectangle. Eve","description":"The correct option is B) A non-parallelogram figures cannot be either a square or a rectangle. Let the statements be: 1. Every square is a rectangle. (Square -> Rectangle) 2. Every rectangle is a parallelogram. (Rectangle -> Parallelogram) 3. Every parallelogram is not necessarily a square. (Parallelogram -\/> Square) From statement 1 and 2, we can form a chain: Square -> Rectangle -> Parallelogram. This implies that every square is a parallelogram. Now let's analyze the conclusions: A) All parallelograms are either squares or rectangles. This is false. A rhombus is a parallelogram but is not necessarily a square or a rectangle. B) A non-parallelogram figures cannot be either a square or a rectangle. This is true. From Rectangle -> Parallelogram, the contrapositive is (Not Parallelogram) -> (Not Rectangle). From Square -> Rectangle, the contrapositive is (Not Rectangle) -> (Not Square). Combining these, if a figure is not a parallelogram, then it is not a rectangle. If it is not a rectangle, then it is not a square. Therefore, if a figure is a non-parallelogram, it cannot be a rectangle, and thus cannot be a square. This conclusion is logically derived from the first two statements. C) All rectangles are either squares or parallelograms. This statement is technically true because all rectangles *are* parallelograms (Statement 2), and the set of squares is a subset of rectangles. So, a rectangle is always in the set of parallelograms, and sometimes in the set of squares. However, the wording \"either...or\" often implies mutual exclusion or at least that being a parallelogram is not always the case for a rectangle, which contradicts statement 2. Conclusion B is a more direct and stronger inference from the combined statements. D) Squares and rectangles are the only parallelograms. This is false. Rhombuses and other non-rectangular parallelograms exist. Conclusion B is the only valid and direct conclusion that can be drawn based on the transitive property implied by the statements.","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\/consider-the-following-statements-every-square-is-a-rectangle-eve\/","og_locale":"en_US","og_type":"article","og_title":"Consider the following statements:  Every square is a rectangle. Eve","og_description":"The correct option is B) A non-parallelogram figures cannot be either a square or a rectangle. Let the statements be: 1. Every square is a rectangle. (Square -> Rectangle) 2. Every rectangle is a parallelogram. (Rectangle -> Parallelogram) 3. Every parallelogram is not necessarily a square. (Parallelogram -\/> Square) From statement 1 and 2, we can form a chain: Square -> Rectangle -> Parallelogram. This implies that every square is a parallelogram. Now let's analyze the conclusions: A) All parallelograms are either squares or rectangles. This is false. A rhombus is a parallelogram but is not necessarily a square or a rectangle. B) A non-parallelogram figures cannot be either a square or a rectangle. This is true. From Rectangle -> Parallelogram, the contrapositive is (Not Parallelogram) -> (Not Rectangle). From Square -> Rectangle, the contrapositive is (Not Rectangle) -> (Not Square). Combining these, if a figure is not a parallelogram, then it is not a rectangle. If it is not a rectangle, then it is not a square. Therefore, if a figure is a non-parallelogram, it cannot be a rectangle, and thus cannot be a square. This conclusion is logically derived from the first two statements. C) All rectangles are either squares or parallelograms. This statement is technically true because all rectangles *are* parallelograms (Statement 2), and the set of squares is a subset of rectangles. So, a rectangle is always in the set of parallelograms, and sometimes in the set of squares. However, the wording \"either...or\" often implies mutual exclusion or at least that being a parallelogram is not always the case for a rectangle, which contradicts statement 2. Conclusion B is a more direct and stronger inference from the combined statements. D) Squares and rectangles are the only parallelograms. This is false. Rhombuses and other non-rectangular parallelograms exist. Conclusion B is the only valid and direct conclusion that can be drawn based on the transitive property implied by the statements.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-statements-every-square-is-a-rectangle-eve\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T09:59:17+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\/consider-the-following-statements-every-square-is-a-rectangle-eve\/","url":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-statements-every-square-is-a-rectangle-eve\/","name":"Consider the following statements: Every square is a rectangle. Eve","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T09:59:17+00:00","dateModified":"2025-06-01T09:59:17+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct option is B) A non-parallelogram figures cannot be either a square or a rectangle. Let the statements be: 1. Every square is a rectangle. (Square -> Rectangle) 2. Every rectangle is a parallelogram. (Rectangle -> Parallelogram) 3. Every parallelogram is not necessarily a square. (Parallelogram -\/> Square) From statement 1 and 2, we can form a chain: Square -> Rectangle -> Parallelogram. This implies that every square is a parallelogram. Now let's analyze the conclusions: A) All parallelograms are either squares or rectangles. This is false. A rhombus is a parallelogram but is not necessarily a square or a rectangle. B) A non-parallelogram figures cannot be either a square or a rectangle. This is true. From Rectangle -> Parallelogram, the contrapositive is (Not Parallelogram) -> (Not Rectangle). From Square -> Rectangle, the contrapositive is (Not Rectangle) -> (Not Square). Combining these, if a figure is not a parallelogram, then it is not a rectangle. If it is not a rectangle, then it is not a square. Therefore, if a figure is a non-parallelogram, it cannot be a rectangle, and thus cannot be a square. This conclusion is logically derived from the first two statements. C) All rectangles are either squares or parallelograms. This statement is technically true because all rectangles *are* parallelograms (Statement 2), and the set of squares is a subset of rectangles. So, a rectangle is always in the set of parallelograms, and sometimes in the set of squares. However, the wording \"either...or\" often implies mutual exclusion or at least that being a parallelogram is not always the case for a rectangle, which contradicts statement 2. Conclusion B is a more direct and stronger inference from the combined statements. D) Squares and rectangles are the only parallelograms. This is false. Rhombuses and other non-rectangular parallelograms exist. Conclusion B is the only valid and direct conclusion that can be drawn based on the transitive property implied by the statements.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-statements-every-square-is-a-rectangle-eve\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-statements-every-square-is-a-rectangle-eve\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-following-statements-every-square-is-a-rectangle-eve\/#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":"Consider the following statements: Every square is a rectangle. Eve"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89222","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=89222"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89222\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}