{"id":45913,"date":"2024-04-15T22:04:51","date_gmt":"2024-04-15T22:04:51","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=45913"},"modified":"2024-04-15T22:04:51","modified_gmt":"2024-04-15T22:04:51","slug":"statements-some-taxis-have-horns-some-taxis-have-lights-conclusions-i-every-taxi-has-either-horn-or-light-ii-some-taxis-have-neither-light-nor-horn-iii-some-taxis-have-horns-as-well-as-ligh","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/statements-some-taxis-have-horns-some-taxis-have-lights-conclusions-i-every-taxi-has-either-horn-or-light-ii-some-taxis-have-neither-light-nor-horn-iii-some-taxis-have-horns-as-well-as-ligh\/","title":{"rendered":"Statements : Some taxis have horns. Some taxis have lights. Conclusions : I. Every taxi has either horn or light. II. Some taxis have neither light nor horn. III. Some taxis have horns as well as lights. IV. No taxi has horn as well as light."},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a97d9b7b7456\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"false\">\r\n                    Only I and II follow                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    Only II and III follow                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"true\">\r\n                    Only II and IV follow                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    Either III or IV follows E. All follow                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is: Only I and II follow.<\/p>\n<p>The first statement, &#8220;Some taxis have horns,&#8221; can be expressed in propositional logic as $p$. The second statement, &#8220;Some taxis have lights,&#8221; can be expressed as $q$. The four conclusions are:<\/p>\n<ul>\n<li>I. Every taxi has <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> either horn or light. This can be expressed in propositional logic as $\\neg p \\lor \\neg q$.<\/li>\n<li>II. Some taxis have neither light nor horn. This can be expressed as $p \\land q$.<\/li>\n<li>III. Some taxis have horns as well as lights. This can be expressed as $p \\land q$.<\/li>\n<li>IV. No taxi has horn as well as light. This can be expressed as $\\neg (p \\land q)$.<\/li>\n<\/ul>\n<p>To determine which conclusions follow from the premises, we can use a truth table. The truth table for the premises is as follows:<\/p>\n<p>p | q | $\\neg p$ | $\\neg q$ | $p \\lor q$ | $p \\land q$ | $p \\land \\neg q$ | $\\neg p \\land q$ | $\\neg p \\land \\neg q$<br \/>\n&#8212; | &#8212; | &#8212; | &#8212; | &#8212; | &#8212; | &#8212; | &#8212; | &#8212;<br \/>\nT | T | F | F | T | T | F | F | F<br \/>\nT | F | T | T | T | F | T | F | F<br \/>\nF | T | T | F | T | T | T | F | F<br \/>\nF | F | T | T | F | F | T | T | T<\/p>\n<p>The first conclusion, $\\neg p \\lor \\neg q$, is true in all rows of the truth table except the first row. This means that the conclusion does not follow from the premises.<\/p>\n<p>The second conclusion, $p \\land q$, is true in the first and third rows of the truth table. This means that the conclusion follows from the premises.<\/p>\n<p>The third conclusion, $p \\land q$, is true in the first and third rows of the truth table. This means that the conclusion follows from the premises.<\/p>\n<p>The fourth conclusion, $\\neg (p \\land q)$, is true in the second and fourth rows of the truth table. This means that the conclusion does not follow from the premises.<\/p>\n<p>Therefore, the only conclusions that follow from the premises are I and II.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[723],"tags":[],"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>Statements : Some taxis have horns. Some taxis have lights. Conclusions : I. Every taxi has either horn or light. II. Some taxis have neither light nor horn. III. Some taxis have horns as well as lights. IV. 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Some taxis have lights. Conclusions : I. Every taxi has either horn or light. II. Some taxis have neither light nor horn. III. Some taxis have horns as well as lights. IV. No taxi has horn as well as light.","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\/statements-some-taxis-have-horns-some-taxis-have-lights-conclusions-i-every-taxi-has-either-horn-or-light-ii-some-taxis-have-neither-light-nor-horn-iii-some-taxis-have-horns-as-well-as-ligh\/","og_locale":"en_US","og_type":"article","og_title":"Statements : Some taxis have horns. Some taxis have lights. Conclusions : I. Every taxi has either horn or light. II. Some taxis have neither light nor horn. III. Some taxis have horns as well as lights. IV. 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No taxi has horn as well as light."}]},{"@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\/d97f17072bfa490596c8f78363955d55?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d97f17072bfa490596c8f78363955d55?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\/45913"}],"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=45913"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/45913\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=45913"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=45913"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=45913"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}