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Statement 1 : The statement A\rightarrow (B\rightarrow A) is equivalent to A\rightarrow (A\vee B) .

Statement 2 : The statement  \sim \left [ \left ( A\wedge B \right )\rightarrow \left ( \sim A\vee B \right ) \right ]  is a Tautology .

Option: 1

Statement 1 is False , Statement 2 is True .


Option: 2

Statement-1 is true; Statement-2 is true; Statement- 2 is not correct explanation for Statement-1.


Option: 3

Statement 1 is True , Statement 2 is False .


Option: 4

Statement-1 is true; Statement-2 is true; Statement- 2 is the correct explanation for Statement-1.


Answers (1)

best_answer

Write the truth table

\begin{array}{|c|c|c|c|c|c|c|} \hline \mathrm{A} & \mathrm{B} & \sim \mathrm{A} & \mathrm{A} \wedge \mathrm{B} & \sim \mathrm{A} \vee \mathrm{B} & \begin{array}{c} (\mathrm{A} \wedge \mathrm{B}) \rightarrow \\ (\sim \mathrm{A} \vee \mathrm{B}) \end{array} & \begin{array}{c} \sim[(\mathrm{A} \wedge \mathrm{B}) \rightarrow \\ (\sim \mathrm{A} \vee \mathrm{B})] \end{array} \\ \hline \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \\ \hline \end{array}

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manish painkra

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