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If p and q are true and r and s are false, find the truth value of the following compound statement. [(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s] - Mathematics and Statistics

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प्रश्न

If p and q are true and r and s are false, find the truth value of the following compound statement.

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]

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उत्तर

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]

≡ [(T ∨ F) → F] ∨ ~[~ (T → T) ∨ F] 

≡ (T → F) ∨ ~ (~ T ∨ F)

≡ F ∨ ~ (F ∨ F)

≡ F ∨ ~ F

≡ F ∨ T

≡ T

Hence, truth value is T.

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अध्याय 1: Mathematical Logic - Exercise 1.4 [पृष्ठ ११]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.4 | Q 3.5 | पृष्ठ ११

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