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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

Sum

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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Solution

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

≡ ~[T ↔ (T ∧ F)] 

≡ ~(T ↔ F)

≡ ~ F

≡ T

Hence, truth value is T.

Concept: Mathematical Logic - Truth Value of Statement in Logic
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.09 | Page 32
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