{"id":90171,"date":"2025-06-01T10:22:13","date_gmt":"2025-06-01T10:22:13","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90171"},"modified":"2025-06-01T10:22:13","modified_gmt":"2025-06-01T10:22:13","slug":"if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/","title":{"rendered":"If all students are boys and all boys are dancers, then which one of t"},"content":{"rendered":"

If all students are boys and all boys are dancers, then which one of the following statements is definitely true?<\/p>\n

[amp_mcq option1=”All dancers are boys” option2=”All boys are students” option3=”All dancers are students” option4=”All students are dancers” correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2017<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe given statements are:
\n1. All students are boys. (If someone is a student, then that person is a boy. Student -> Boy)
\n2. All boys are dancers. (If someone is a boy, then that person is a dancer. Boy -> Dancer)
\nWe can combine these two conditional statements using the principle of transitivity:
\nIf Student -> Boy and Boy -> Dancer, then it logically follows that Student -> Dancer.
\nThis means, “If someone is a student, then that person is a dancer,” which can be rephrased as “All students are dancers.”
\nLet’s examine the options based on this deduction:
\nA) All dancers are boys (Dancer -> Boy). This is the converse of “All boys are dancers” and is not necessarily true.
\nB) All boys are students (Boy -> Student). This is the converse of “All students are boys” and is not necessarily true.
\nC) All dancers are students (Dancer -> Student). This is the converse of the derived conclusion “All students are dancers” and is not necessarily true.
\nD) All students are dancers (Student -> Dancer). This is the direct logical conclusion derived from the premises.
\n<\/section>\n
\nThis problem requires understanding logical implication and how to chain conditional statements (syllogism). If P implies Q, and Q implies R, then P implies R.
\n<\/section>\n
\nUsing Venn diagrams can also help visualize this. Draw a circle for ‘Students’ inside a circle for ‘Boys’. Then draw the ‘Boys’ circle inside a larger circle for ‘Dancers’. It becomes clear that the ‘Students’ circle is entirely contained within the ‘Dancers’ circle, meaning all students are dancers. The reverse relationships (e.g., all dancers are boys) are not guaranteed, as there can be dancers who are not boys (and thus not students).
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

If all students are boys and all boys are dancers, then which one of the following statements is definitely true? [amp_mcq option1=”All dancers are boys” option2=”All boys are students” option3=”All dancers are students” option4=”All students are dancers” correct=”option4″] This question was previously asked in UPSC CAPF – 2017 Download PDFAttempt Online The given statements are: … <\/p>\n

Detailed SolutionIf all students are boys and all boys are dancers, then which one of t<\/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":[1101,1102],"class_list":["post-90171","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1101","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIf all students are boys and all boys are dancers, then which one of t<\/title>\n<meta name=\"description\" content=\"The given statements are: 1. All students are boys. (If someone is a student, then that person is a boy. Student -> Boy) 2. All boys are dancers. (If someone is a boy, then that person is a dancer. Boy -> Dancer) We can combine these two conditional statements using the principle of transitivity: If Student -> Boy and Boy -> Dancer, then it logically follows that Student -> Dancer. This means, "If someone is a student, then that person is a dancer," which can be rephrased as "All students are dancers." Let's examine the options based on this deduction: A) All dancers are boys (Dancer -> Boy). This is the converse of "All boys are dancers" and is not necessarily true. B) All boys are students (Boy -> Student). This is the converse of "All students are boys" and is not necessarily true. C) All dancers are students (Dancer -> Student). This is the converse of the derived conclusion "All students are dancers" and is not necessarily true. D) All students are dancers (Student -> Dancer). This is the direct logical conclusion derived from the premises. This problem requires understanding logical implication and how to chain conditional statements (syllogism). If P implies Q, and Q implies R, then P implies R.\" \/>\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\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If all students are boys and all boys are dancers, then which one of t\" \/>\n<meta property=\"og:description\" content=\"The given statements are: 1. All students are boys. (If someone is a student, then that person is a boy. Student -> Boy) 2. All boys are dancers. (If someone is a boy, then that person is a dancer. Boy -> Dancer) We can combine these two conditional statements using the principle of transitivity: If Student -> Boy and Boy -> Dancer, then it logically follows that Student -> Dancer. This means, "If someone is a student, then that person is a dancer," which can be rephrased as "All students are dancers." Let's examine the options based on this deduction: A) All dancers are boys (Dancer -> Boy). This is the converse of "All boys are dancers" and is not necessarily true. B) All boys are students (Boy -> Student). This is the converse of "All students are boys" and is not necessarily true. C) All dancers are students (Dancer -> Student). This is the converse of the derived conclusion "All students are dancers" and is not necessarily true. D) All students are dancers (Student -> Dancer). This is the direct logical conclusion derived from the premises. This problem requires understanding logical implication and how to chain conditional statements (syllogism). If P implies Q, and Q implies R, then P implies R.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:22:13+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":"If all students are boys and all boys are dancers, then which one of t","description":"The given statements are: 1. All students are boys. (If someone is a student, then that person is a boy. Student -> Boy) 2. All boys are dancers. (If someone is a boy, then that person is a dancer. Boy -> Dancer) We can combine these two conditional statements using the principle of transitivity: If Student -> Boy and Boy -> Dancer, then it logically follows that Student -> Dancer. This means, \"If someone is a student, then that person is a dancer,\" which can be rephrased as \"All students are dancers.\" Let's examine the options based on this deduction: A) All dancers are boys (Dancer -> Boy). This is the converse of \"All boys are dancers\" and is not necessarily true. B) All boys are students (Boy -> Student). This is the converse of \"All students are boys\" and is not necessarily true. C) All dancers are students (Dancer -> Student). This is the converse of the derived conclusion \"All students are dancers\" and is not necessarily true. D) All students are dancers (Student -> Dancer). This is the direct logical conclusion derived from the premises. This problem requires understanding logical implication and how to chain conditional statements (syllogism). If P implies Q, and Q implies R, then P implies R.","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\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/","og_locale":"en_US","og_type":"article","og_title":"If all students are boys and all boys are dancers, then which one of t","og_description":"The given statements are: 1. All students are boys. (If someone is a student, then that person is a boy. Student -> Boy) 2. All boys are dancers. (If someone is a boy, then that person is a dancer. Boy -> Dancer) We can combine these two conditional statements using the principle of transitivity: If Student -> Boy and Boy -> Dancer, then it logically follows that Student -> Dancer. This means, \"If someone is a student, then that person is a dancer,\" which can be rephrased as \"All students are dancers.\" Let's examine the options based on this deduction: A) All dancers are boys (Dancer -> Boy). This is the converse of \"All boys are dancers\" and is not necessarily true. B) All boys are students (Boy -> Student). This is the converse of \"All students are boys\" and is not necessarily true. C) All dancers are students (Dancer -> Student). This is the converse of the derived conclusion \"All students are dancers\" and is not necessarily true. D) All students are dancers (Student -> Dancer). This is the direct logical conclusion derived from the premises. This problem requires understanding logical implication and how to chain conditional statements (syllogism). If P implies Q, and Q implies R, then P implies R.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:22:13+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\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/","name":"If all students are boys and all boys are dancers, then which one of t","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:22:13+00:00","dateModified":"2025-06-01T10:22:13+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The given statements are: 1. All students are boys. (If someone is a student, then that person is a boy. Student -> Boy) 2. All boys are dancers. (If someone is a boy, then that person is a dancer. Boy -> Dancer) We can combine these two conditional statements using the principle of transitivity: If Student -> Boy and Boy -> Dancer, then it logically follows that Student -> Dancer. This means, \"If someone is a student, then that person is a dancer,\" which can be rephrased as \"All students are dancers.\" Let's examine the options based on this deduction: A) All dancers are boys (Dancer -> Boy). This is the converse of \"All boys are dancers\" and is not necessarily true. B) All boys are students (Boy -> Student). This is the converse of \"All students are boys\" and is not necessarily true. C) All dancers are students (Dancer -> Student). This is the converse of the derived conclusion \"All students are dancers\" and is not necessarily true. D) All students are dancers (Student -> Dancer). This is the direct logical conclusion derived from the premises. This problem requires understanding logical implication and how to chain conditional statements (syllogism). If P implies Q, and Q implies R, then P implies R.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-all-students-are-boys-and-all-boys-are-dancers-then-which-one-of-t\/#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":"If all students are boys and all boys are dancers, then which one of t"}]},{"@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\/90171","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=90171"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90171\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}