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If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following. ∼ [(p → q) ↔ (p ∧ ∼ q)] - Mathematics and Statistics

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प्रश्न

If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.

∼ [(p → q) ↔ (p ∧ ∼ q)]

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उत्तर

∼[(p → q) ↔ (p ∧ ∼q)] ≡ ∼ [(T → T) ↔ (T ∧ ∼ T)]

≡ ~[T ↔ (T ∧ F)] 

≡ ~(T ↔ F)

≡ ~ F

≡ T

Hence, truth value is T.

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पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३२]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.09 | पृष्ठ ३२
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