{"id":89463,"date":"2025-06-01T10:05:08","date_gmt":"2025-06-01T10:05:08","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89463"},"modified":"2025-06-01T10:05:08","modified_gmt":"2025-06-01T10:05:08","slug":"if-it-is-true-that-all-pollutants-are-harmful-identify-which-of-the","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-it-is-true-that-all-pollutants-are-harmful-identify-which-of-the\/","title":{"rendered":"If it is true that ‘all pollutants are harmful’, identify which of the"},"content":{"rendered":"

If it is true that ‘all pollutants are harmful’, identify which of the following is invalid to infer from it?<\/p>\n

[amp_mcq option1=”Pollutants constitute a subset of harmful things” option2=”No pollutants are non-harmful” option3=”If anything is harmful, it is a pollutant” option4=”Some pollutants are harmful” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2011<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe given statement is “all pollutants are harmful”. This is a universal affirmative statement (All P are H, where P=Pollutants, H=Harmful). We need to identify which inference is invalid.
\nA) Pollutants constitute a subset of harmful things: This means every pollutant is a harmful thing, which is exactly what “all pollutants are harmful” means. This is a valid inference.
\nB) No pollutants are non-harmful: This means that it is not the case that some pollutants are not harmful, which implies all pollutants are harmful. This is the obversion of the original statement and is a valid inference.
\nC) If anything is harmful, it is a pollutant: This means “all harmful things are pollutants” (All H are P). This is the converse of the original statement “All P are H”. The converse of a universal affirmative statement is not necessarily true. For example, fire might be harmful, but it is not typically classified as a pollutant in the same category as, say, smoke or chemicals. This is an invalid inference.
\nD) Some pollutants are harmful: This is a particular affirmative statement (Some P are H). If “All P are H” is true (assuming there are pollutants), then “Some P are H” must also be true. This is a valid inference by subalternation.
\n<\/section>\n
\nUnderstanding logical inferences from universal affirmative statements (All A are B). Valid inferences include obversion (No A are non-B) and subalternation (Some A are B). The converse (All B are A) and inverse (All non-A are non-B) are generally not valid inferences.
\n<\/section>\n
\nIn formal logic, this relates to the square of opposition and immediate inferences. The truth of a universal statement (All A are B) guarantees the truth of its subaltern (Some A are B) and its obverse (No A are non-B), but not necessarily its converse (All B are A) or contrapositive (All non-B are non-A), though the contrapositive IS valid if the original statement is true. In this case, the converse (C) is requested as the invalid inference.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

If it is true that ‘all pollutants are harmful’, identify which of the following is invalid to infer from it? [amp_mcq option1=”Pollutants constitute a subset of harmful things” option2=”No pollutants are non-harmful” option3=”If anything is harmful, it is a pollutant” option4=”Some pollutants are harmful” correct=”option3″] This question was previously asked in UPSC CAPF – 2011 … <\/p>\n

Detailed SolutionIf it is true that ‘all pollutants are harmful’, identify which of the<\/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":[1465,1102],"class_list":["post-89463","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1465","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIf it is true that 'all pollutants are harmful', identify which of the<\/title>\n<meta name=\"description\" content=\"The given statement is "all pollutants are harmful". This is a universal affirmative statement (All P are H, where P=Pollutants, H=Harmful). We need to identify which inference is invalid. A) Pollutants constitute a subset of harmful things: This means every pollutant is a harmful thing, which is exactly what "all pollutants are harmful" means. This is a valid inference. B) No pollutants are non-harmful: This means that it is not the case that some pollutants are not harmful, which implies all pollutants are harmful. This is the obversion of the original statement and is a valid inference. C) If anything is harmful, it is a pollutant: This means "all harmful things are pollutants" (All H are P). This is the converse of the original statement "All P are H". The converse of a universal affirmative statement is not necessarily true. For example, fire might be harmful, but it is not typically classified as a pollutant in the same category as, say, smoke or chemicals. This is an invalid inference. D) Some pollutants are harmful: This is a particular affirmative statement (Some P are H). If "All P are H" is true (assuming there are pollutants), then "Some P are H" must also be true. This is a valid inference by subalternation. Understanding logical inferences from universal affirmative statements (All A are B). Valid inferences include obversion (No A are non-B) and subalternation (Some A are B). The converse (All B are A) and inverse (All non-A are non-B) are generally not valid inferences.\" \/>\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-it-is-true-that-all-pollutants-are-harmful-identify-which-of-the\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If it is true that 'all pollutants are harmful', identify which of the\" \/>\n<meta property=\"og:description\" content=\"The given statement is "all pollutants are harmful". This is a universal affirmative statement (All P are H, where P=Pollutants, H=Harmful). We need to identify which inference is invalid. A) Pollutants constitute a subset of harmful things: This means every pollutant is a harmful thing, which is exactly what "all pollutants are harmful" means. This is a valid inference. B) No pollutants are non-harmful: This means that it is not the case that some pollutants are not harmful, which implies all pollutants are harmful. This is the obversion of the original statement and is a valid inference. C) If anything is harmful, it is a pollutant: This means "all harmful things are pollutants" (All H are P). This is the converse of the original statement "All P are H". The converse of a universal affirmative statement is not necessarily true. For example, fire might be harmful, but it is not typically classified as a pollutant in the same category as, say, smoke or chemicals. This is an invalid inference. D) Some pollutants are harmful: This is a particular affirmative statement (Some P are H). If "All P are H" is true (assuming there are pollutants), then "Some P are H" must also be true. This is a valid inference by subalternation. Understanding logical inferences from universal affirmative statements (All A are B). Valid inferences include obversion (No A are non-B) and subalternation (Some A are B). The converse (All B are A) and inverse (All non-A are non-B) are generally not valid inferences.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-it-is-true-that-all-pollutants-are-harmful-identify-which-of-the\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:05:08+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 it is true that 'all pollutants are harmful', identify which of the","description":"The given statement is \"all pollutants are harmful\". This is a universal affirmative statement (All P are H, where P=Pollutants, H=Harmful). We need to identify which inference is invalid. A) Pollutants constitute a subset of harmful things: This means every pollutant is a harmful thing, which is exactly what \"all pollutants are harmful\" means. This is a valid inference. B) No pollutants are non-harmful: This means that it is not the case that some pollutants are not harmful, which implies all pollutants are harmful. This is the obversion of the original statement and is a valid inference. C) If anything is harmful, it is a pollutant: This means \"all harmful things are pollutants\" (All H are P). This is the converse of the original statement \"All P are H\". The converse of a universal affirmative statement is not necessarily true. For example, fire might be harmful, but it is not typically classified as a pollutant in the same category as, say, smoke or chemicals. This is an invalid inference. D) Some pollutants are harmful: This is a particular affirmative statement (Some P are H). If \"All P are H\" is true (assuming there are pollutants), then \"Some P are H\" must also be true. This is a valid inference by subalternation. Understanding logical inferences from universal affirmative statements (All A are B). Valid inferences include obversion (No A are non-B) and subalternation (Some A are B). The converse (All B are A) and inverse (All non-A are non-B) are generally not valid inferences.","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-it-is-true-that-all-pollutants-are-harmful-identify-which-of-the\/","og_locale":"en_US","og_type":"article","og_title":"If it is true that 'all pollutants are harmful', identify which of the","og_description":"The given statement is \"all pollutants are harmful\". This is a universal affirmative statement (All P are H, where P=Pollutants, H=Harmful). We need to identify which inference is invalid. A) Pollutants constitute a subset of harmful things: This means every pollutant is a harmful thing, which is exactly what \"all pollutants are harmful\" means. This is a valid inference. B) No pollutants are non-harmful: This means that it is not the case that some pollutants are not harmful, which implies all pollutants are harmful. This is the obversion of the original statement and is a valid inference. C) If anything is harmful, it is a pollutant: This means \"all harmful things are pollutants\" (All H are P). This is the converse of the original statement \"All P are H\". The converse of a universal affirmative statement is not necessarily true. For example, fire might be harmful, but it is not typically classified as a pollutant in the same category as, say, smoke or chemicals. This is an invalid inference. D) Some pollutants are harmful: This is a particular affirmative statement (Some P are H). If \"All P are H\" is true (assuming there are pollutants), then \"Some P are H\" must also be true. This is a valid inference by subalternation. Understanding logical inferences from universal affirmative statements (All A are B). Valid inferences include obversion (No A are non-B) and subalternation (Some A are B). The converse (All B are A) and inverse (All non-A are non-B) are generally not valid inferences.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-it-is-true-that-all-pollutants-are-harmful-identify-which-of-the\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:05:08+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-it-is-true-that-all-pollutants-are-harmful-identify-which-of-the\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-it-is-true-that-all-pollutants-are-harmful-identify-which-of-the\/","name":"If it is true that 'all pollutants are harmful', identify which of the","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:05:08+00:00","dateModified":"2025-06-01T10:05:08+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The given statement is \"all pollutants are harmful\". This is a universal affirmative statement (All P are H, where P=Pollutants, H=Harmful). We need to identify which inference is invalid. A) Pollutants constitute a subset of harmful things: This means every pollutant is a harmful thing, which is exactly what \"all pollutants are harmful\" means. This is a valid inference. B) No pollutants are non-harmful: This means that it is not the case that some pollutants are not harmful, which implies all pollutants are harmful. This is the obversion of the original statement and is a valid inference. C) If anything is harmful, it is a pollutant: This means \"all harmful things are pollutants\" (All H are P). This is the converse of the original statement \"All P are H\". The converse of a universal affirmative statement is not necessarily true. For example, fire might be harmful, but it is not typically classified as a pollutant in the same category as, say, smoke or chemicals. This is an invalid inference. D) Some pollutants are harmful: This is a particular affirmative statement (Some P are H). If \"All P are H\" is true (assuming there are pollutants), then \"Some P are H\" must also be true. This is a valid inference by subalternation. Understanding logical inferences from universal affirmative statements (All A are B). Valid inferences include obversion (No A are non-B) and subalternation (Some A are B). 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