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If the statement p, q are true statement and r, s are false statement then determine the truth value of the following: (∼ r ↔ p) → ∼ q - Mathematics and Statistics

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प्रश्न

If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(∼ r ↔ p) → ∼ q

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उत्तर

Truth values of p and q are T and truth values of r and s are F.

(∼ r ↔ p) → (∼ q) ≡ ( ∼ F ↔ T) → (∼ T)
                             ≡ (T ↔ T) →F
                             ≡ T→ F ≡ F
Hence the truth value of the given statement is false.

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पाठ 1: Mathematical Logic - Exercise 1.1 [पृष्ठ ७]

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