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<blockquote data-quote="rukshan86" data-source="post: 28943034" data-attributes="member: 84993"><p>Mata nam therenne ne eth mamath try ekak dunna machan Chat GPT labben. meka thama result eka awe.</p><p></p><p>1.) First-order logic representation:</p><p></p><p>L(x) - "x owns lands" V(x) - "x owns vehicles" T(x) - "x pays tax"</p><p></p><p>∀x (L(x) ∨ V(x) → T(x)) ∃x (¬V(x) ∧ T(x)) ¬∃x T(x)</p><p></p><p>Conjunctive normal form (CNF):</p><p></p><p>(¬L(x) ∨ ¬V(x) ∨ T(x)) (¬V(x) ∨ T(x)) ¬T(x)</p><p></p><p>2.) Sarath argues that Kamal does not own a vehicle. To justify this using the method of contradiction, let's assume that Kamal does own a vehicle (V(Kamal)).</p><p></p><p>From the given information, we have: ∀x (L(x) ∨ V(x) → T(x)) ∃x (¬V(x) ∧ T(x)) ¬∃x T(x)</p><p></p><p>By substituting Kamal for x, we can derive the following: (L(Kamal) ∨ V(Kamal) → T(Kamal)) (¬V(Kamal) ∧ T(Kamal)) ¬T(Kamal)</p><p></p><p>Now, we have the assumption V(Kamal) and the derived statement (¬V(Kamal) ∧ T(Kamal)). This leads to a contradiction since Kamal cannot both own a vehicle and not own a vehicle at the same time.</p><p></p><p>Therefore, based on the method of contradiction, we can conclude that Sarath's argument is correct, and Kamal does not own a vehicle.</p></blockquote><p></p>
[QUOTE="rukshan86, post: 28943034, member: 84993"] Mata nam therenne ne eth mamath try ekak dunna machan Chat GPT labben. meka thama result eka awe. 1.) First-order logic representation: L(x) - "x owns lands" V(x) - "x owns vehicles" T(x) - "x pays tax" ∀x (L(x) ∨ V(x) → T(x)) ∃x (¬V(x) ∧ T(x)) ¬∃x T(x) Conjunctive normal form (CNF): (¬L(x) ∨ ¬V(x) ∨ T(x)) (¬V(x) ∨ T(x)) ¬T(x) 2.) Sarath argues that Kamal does not own a vehicle. To justify this using the method of contradiction, let's assume that Kamal does own a vehicle (V(Kamal)). From the given information, we have: ∀x (L(x) ∨ V(x) → T(x)) ∃x (¬V(x) ∧ T(x)) ¬∃x T(x) By substituting Kamal for x, we can derive the following: (L(Kamal) ∨ V(Kamal) → T(Kamal)) (¬V(Kamal) ∧ T(Kamal)) ¬T(Kamal) Now, we have the assumption V(Kamal) and the derived statement (¬V(Kamal) ∧ T(Kamal)). This leads to a contradiction since Kamal cannot both own a vehicle and not own a vehicle at the same time. Therefore, based on the method of contradiction, we can conclude that Sarath's argument is correct, and Kamal does not own a vehicle. [/QUOTE]
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