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  • Among the statements : <img alt="(S 1)((p \vee q) \Rightarrow r) \Leftrightarrow(p \Rightarrow r)" src="https://entrancecorner.oncodecogs.com/gif.latex?%28S%201%29%28%28p%20%5Cvee%20q%29%

Among the statements :

(S 1)((p \vee q) \Rightarrow r) \Leftrightarrow(p \Rightarrow r)

(S 2)((p \vee q) \Rightarrow r) \Leftrightarrow((p \Rightarrow r) V(q \Rightarrow r))

 

Option: 1

only (S2) is a tautology


Option: 2

only (S1) is a tautology


Option: 3

neither ( S1) nor (S2) is a tautology


Option: 4

both (S1) and (S2) are tautologies


Answers (1)

best_answer

\begin{aligned} & S_1:((p \vee q) \Rightarrow r) \Leftrightarrow(p \Rightarrow r) \\ & p \quad q \quad r \quad \begin{array}{l} (p \vee q) \Rightarrow r \\ (\sim p \wedge \sim q) \vee r \end{array} \sim p \vee r \quad((p \vee q) \Rightarrow r) \Leftrightarrow(p \Rightarrow r) \end{aligned}

S_{1} is not a tautology 

S_2=((p \vee q) \Rightarrow r) \Leftrightarrow((p \Rightarrow r) \vee(q \Rightarrow r))

S_2 is not a tautology
So, neither S_1 nor S_2 is a tautology.

Posted by

sudhir.kumar

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