{"id":2940,"date":"2025-06-06T07:03:32","date_gmt":"2025-06-06T07:03:32","guid":{"rendered":"https:\/\/diznr.com\/?p=2940"},"modified":"2025-06-06T07:03:32","modified_gmt":"2025-06-06T07:03:32","slug":"statement-based-problem-on-proposition-gate-2021-discrete-consider-the-statements-following","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/statement-based-problem-on-proposition-gate-2021-discrete-consider-the-statements-following\/","title":{"rendered":". Statement based Problem on Proposition- GATE 2025 Discrete Consider the following statements"},"content":{"rendered":"

. Statement based Problem on Proposition- GATE 2025 Discrete Consider the following statements<\/p>\n

[fvplayer id=”180″]<\/p>\n

\u0915\u0943\u092a\u092f\u093e \u092a\u0942\u0930\u093e \u092a\u094d\u0930\u0936\u094d\u0928 \u0938\u093e\u091d\u093e \u0915\u0930\u0947\u0902 \u0924\u093e\u0915\u093f \u092e\u0948\u0902 GATE 2025 Discrete Mathematics<\/strong> (Propositional Logic) \u0915\u0947 Statement-based Problem<\/strong> \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0906\u092a\u0915\u0940 \u092e\u0926\u0926 \u0915\u0930 \u0938\u0915\u0942\u0901\u0964<\/p>\n

\u0905\u0917\u0930 \u092f\u0939 \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0915\u0925\u0928\u094b\u0902 (Logical Statements)<\/strong>, \u0938\u0924\u094d\u092f \u0938\u093e\u0930\u0923\u0940 (Truth Table)<\/strong>, \u092a\u0930\u093f\u0923\u093e\u092e (Implication)<\/strong> \u092f\u093e \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u092a\u094d\u0930\u092e\u0947\u092f (Logical Theorems)<\/strong> \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948, \u0924\u094b \u092e\u0948\u0902 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0939\u0932 \u0914\u0930 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0926\u0947 \u0938\u0915\u0924\u093e \u0939\u0942\u0901\u0964<\/p>\n

. Statement based Problem on Proposition- GATE 2025 Discrete Consider the following statements<\/a><\/h3>\n

Information Brochure – GATE 2025 – IIT Roorkee<\/a><\/h3>\n

Discrete Mathematics for Computer Science<\/a><\/h3>\n

Here\u2019s a sample Statement-based Problem<\/strong> on Propositions (Logic)<\/strong> in Discrete Mathematics<\/strong>, commonly seen in GATE exams<\/strong> (like GATE 2025). These questions test your understanding of propositional logic, truth values, and logical equivalence.<\/p>\n

\n

\ud83e\udde0 Sample GATE-Style Question on Proposition<\/strong><\/h3>\n

Question:<\/strong>
Consider the following two statements:<\/p>\n

    \n
  • \n

    P<\/strong>: If it rains, then the ground gets wet.<\/p>\n<\/li>\n

  • \n

    Q<\/strong>: The ground is not wet.<\/p>\n<\/li>\n<\/ul>\n

    Which of the following conclusions is logically valid?<\/p>\n

    A. It did not rain
    B. It rained
    C. It rained and the ground is dry
    D. Nothing can be concluded<\/p>\n

    \n

    \u2705 Solution:<\/strong><\/h3>\n

    Convert the statements into propositional logic:<\/p>\n

      \n
    • \n

      Let R<\/strong> = “It rains”<\/p>\n<\/li>\n

    • \n

      Let W<\/strong> = “The ground gets wet”<\/p>\n<\/li>\n<\/ul>\n

      So,<\/p>\n

        \n
      • \n

        P<\/strong>: R\u2192WR \\rightarrow W<\/span>R<\/span>\u2192<\/span><\/span>W<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n

      • \n

        Q<\/strong>: \u00acW\\lnot W<\/span>\u00ac<\/span>W<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

        From P<\/strong> and Q<\/strong>, can we infer anything?<\/p>\n

        From logic:<\/p>\n

          \n
        • \n

          R\u2192WR \\rightarrow W<\/span>R<\/span>\u2192<\/span><\/span>W<\/span><\/span><\/span><\/span> and \u00acW\\lnot W<\/span>\u00ac<\/span>W<\/span><\/span><\/span><\/span>
          \u27f9 By Contrapositive Rule<\/strong>, \u00acW\u2192\u00acR\\lnot W \\rightarrow \\lnot R<\/span>\u00ac<\/span>W<\/span>\u2192<\/span><\/span>\u00ac<\/span>R<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n

          So, \u00acR\\lnot R<\/span>\u00ac<\/span>R<\/span><\/span><\/span><\/span> is true.<\/p>\n

          \n

          \ud83d\udfe9 Correct Answer: A. It did not rain<\/strong><\/h3>\n
          \n

          \ud83d\udccc Tips for Solving These in GATE:<\/h3>\n
            \n
          • \n

            Convert English sentences to propositional logic<\/p>\n<\/li>\n

          • \n

            Use rules like contrapositive<\/strong>, modus ponens<\/strong>, modus tollens<\/strong><\/p>\n<\/li>\n

          • \n

            Carefully identify assumptions vs. conclusions<\/p>\n<\/li>\n<\/ul>\n

            \n

            Would you like more such GATE-style problems with explanations in Hindi<\/strong>, or a PDF worksheet<\/strong> of practice questions?<\/p>\n","protected":false},"excerpt":{"rendered":"

            . Statement based Problem on Proposition- GATE 2025 Discrete Consider the following statements [fvplayer id=”180″] \u0915\u0943\u092a\u092f\u093e \u092a\u0942\u0930\u093e \u092a\u094d\u0930\u0936\u094d\u0928 \u0938\u093e\u091d\u093e \u0915\u0930\u0947\u0902 \u0924\u093e\u0915\u093f \u092e\u0948\u0902 GATE 2025 Discrete Mathematics (Propositional Logic) \u0915\u0947 Statement-based Problem \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0906\u092a\u0915\u0940 \u092e\u0926\u0926 \u0915\u0930 \u0938\u0915\u0942\u0901\u0964 \u0905\u0917\u0930 \u092f\u0939 \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0915\u0925\u0928\u094b\u0902 (Logical Statements), \u0938\u0924\u094d\u092f \u0938\u093e\u0930\u0923\u0940 (Truth Table), \u092a\u0930\u093f\u0923\u093e\u092e (Implication) \u092f\u093e \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u092a\u094d\u0930\u092e\u0947\u092f (Logical […]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[76],"tags":[],"class_list":["post-2940","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2940","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=2940"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2940\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2940"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2940"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2940"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}