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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 ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]

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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 ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]

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उत्तर

~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]

≡ ~ [T ∨ (F ∧ F)] ∧ ~ [(F ∧ ~ F) ∧ T]

≡ ~ (T ∨ F) ∧ ~ [(F ∧ T) ∧ T]

≡ ~ T ∧ ~ (F ∧ T)

≡ F ∧ ~ F

≡ F ∧ T

≡ F

Hence, truth value is F.

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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 3.6 | पृष्ठ ११

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