Previous year gate paper Discrete Mathematics Gate 2025Consider the following expressions.<\/p>\n
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Certainly! Let’s delve into a notable GATE CSE previous year question on Discrete Mathematics<\/strong>, specifically focusing on Propositional Logic<\/strong>:<\/p>\n Question:<\/strong><\/p>\n Consider the following expressions:<\/p>\n (i)<\/strong> false<\/p>\n<\/li>\n (ii)<\/strong> Q<\/p>\n<\/li>\n (iii)<\/strong> true<\/p>\n<\/li>\n (iv)<\/strong> P \u2228 Q<\/p>\n<\/li>\n (v)<\/strong> \u00acQ \u2228 P<\/p>\n<\/li>\n<\/ol>\n How many of the above expressions are logically implied<\/strong> by the expression: We are given the expression: Let’s analyze what this implies:<\/p>\n P<\/strong> is true.<\/p>\n<\/li>\n P \u21d2 Q<\/strong> is true.<\/p>\n<\/li>\n<\/ul>\n From the implication P \u21d2 Q<\/strong>, and knowing that P<\/strong> is true, it follows that Q<\/strong> must also be true. This is based on the truth table of implication, where the only case P \u21d2 Q<\/strong> is false is when P<\/strong> is true and Q<\/strong> is false.<\/p>\n Therefore, from P \u2227 (P \u21d2 Q)<\/strong>, we can deduce:<\/p>\n P<\/strong> is true.<\/p>\n<\/li>\n Q<\/strong> is true.<\/p>\n<\/li>\n<\/ul>\n Now, let’s evaluate each of the given expressions:<\/p>\n (i) false<\/strong><\/p>\n This is a constant false value. Since we have deduced that both P<\/strong> and Q<\/strong> are true, we cannot conclude that false<\/strong> is implied. (ii) Q<\/strong><\/p>\n We have deduced that Q<\/strong> is true. (iii) true<\/strong><\/p>\n A tautology; always true. Since our premises lead to true statements, this is trivially implied. (iv) P \u2228 Q<\/strong><\/p>\n Since both P<\/strong> and Q<\/strong> are true, their disjunction is also true. (v) \u00acQ \u2228 P<\/strong><\/p>\n Let’s evaluate:<\/p>\n \u00acQ<\/strong> is false (since Q<\/strong> is true).<\/p>\n<\/li>\n P<\/strong> is true.<\/p>\n<\/li>\n Therefore, \u00acQ \u2228 P<\/strong> = false \u2228 true = true. 4 expressions<\/strong> are logically implied by P \u2227 (P \u21d2 Q)<\/strong>:<\/span> To strengthen your understanding of Discrete Mathematics for GATE, consider exploring the following resources:<\/p>\n GeeksforGeeks \u2013 Discrete Mathematics GATE Questions:<\/strong> A comprehensive collection of previous year questions with explanations.<\/span><\/p>\n<\/li>\n Examside \u2013 Topic-wise GATE CSE Questions:<\/strong> Offers categorized questions for focused practice.<\/span><\/p>\n<\/li>\n PracticePaper \u2013 Discrete Mathematics for GATE CSE:<\/strong> Provides practice questions with solutions to test your knowledge.<\/span><\/p>\n<\/li>\n<\/ul>\n For a visual and in-depth explanation, you might find the following video helpful:<\/p>\n
\n\ud83e\udde9 GATE CSE 2025 (Set 2) \u2013 Propositional Logic Question<\/strong><\/h3>\n
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P \u2227 (P \u21d2 Q)<\/strong>?<\/p>\n
\n\u2705 Solution:<\/strong><\/h3>\n
P \u2227 (P \u21d2 Q)<\/strong><\/p>\n\n
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\u21d2 Not implied<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n\n
\u21d2 Implied<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n\n
\u21d2 Implied<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n\n
\u21d2 Implied<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n\n
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\u21d2 Implied<\/strong><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n
\n\u2705 Answer:<\/strong><\/h3>\n
(ii) Q, (iii) true, (iv) P \u2228 Q, and (v) \u00acQ \u2228 P.<\/span><\/p>\n
\n\ud83d\udcd8 Further Practice:<\/strong><\/h3>\n
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\ud83c\udfa5 Video Resources:<\/strong><\/h3>\n