{"id":49090,"date":"2024-04-15T22:50:45","date_gmt":"2024-04-15T22:50:45","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=49090"},"modified":"2024-04-15T22:50:45","modified_gmt":"2024-04-15T22:50:45","slug":"statements-some-dogs-are-rats-all-rats-are-trees-some-trees-are-not-dogs-conclusions-i-some-trees-are-dogs-ii-all-dogs-are-trees-iii-all-rats-are-dogs-iv-no-tree-is-dog","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/statements-some-dogs-are-rats-all-rats-are-trees-some-trees-are-not-dogs-conclusions-i-some-trees-are-dogs-ii-all-dogs-are-trees-iii-all-rats-are-dogs-iv-no-tree-is-dog\/","title":{"rendered":"Statements : Some dogs are rats. All rats are trees. Some trees are not dogs. Conclusions : I. Some trees are dogs. II. All dogs are trees. III. All rats are dogs. IV. No tree is dog."},"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_6a974161bfaa8\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    None follows                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    Only I follows                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    Only I and II follow                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    Only II and III follow 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 A. None follows.<\/p>\n<p>The first statement, &#8220;Some dogs are rats,&#8221; can be expressed in symbolic form as $D \\cap R \\neq \\emptyset$. The second statement, &#8220;All rats are trees,&#8221; can be expressed in symbolic form as $R \\subseteq T$. The third statement, &#8220;Some trees are not dogs,&#8221; can be expressed in symbolic form as $T \\setminus D \\neq \\emptyset$.<\/p>\n<p>We can use DeMorgan&#8217;s Law to negate the second statement: $\\neg (R \\subseteq T) \\equiv T \\setminus R \\neq \\emptyset$. This means that there are some trees that are not rats.<\/p>\n<p>We can also use DeMorgan&#8217;s Law to negate the third statement: $\\neg (T \\setminus D \\neq \\emptyset) \\equiv T \\cap D \\neq \\emptyset$. This <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\" 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      <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>       Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> means that there are some trees that are dogs.<\/p>\n<p>However, we cannot conclude that all trees are dogs, all dogs are trees, or all rats are dogs. This is because the first statement only tells us that some dogs are rats, and the second statement only tells us that all rats are trees. It is possible that there are dogs that are not rats, and it is also possible that there are trees that are not rats.<\/p>\n<p>Therefore, none of the conclusions follow.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel 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 dogs are rats. All rats are trees. Some trees are not dogs. Conclusions : I. Some trees are dogs. II. All dogs are trees. III. All rats are dogs. IV. 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