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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Prove that the following statement pattern is a tautology. (~p ∧ ~q ) → (p → q) - Mathematics and Statistics

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प्रश्न

Prove that the following statement pattern is a tautology.

(~p ∧ ~q ) → (p → q)

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उत्तर

p q ~p ~q ~p∧~q p→q (~p∧~q)→(p→q)
T T F F F T T
T F F T F F T
F T T F F T T
F F T T T T T

All the truth values in the last column are T. Hence, it is a tautology.

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पाठ 1: Mathematical Logic - Exercise 1.6 [पृष्ठ १६]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Exercise 1.6 | Q 3.3 | पृष्ठ १६
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