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Mathematical Reasoning
hard
Statement $-1$ : The statement $A \to (B \to A)$ is equivalent to $A \to \left( {A \vee B} \right)$.
Statement $-2$ : The statement $ \sim \left[ {\left( {A \wedge B} \right) \to \left( { \sim A \vee B} \right)} \right]$ is a Tautology
A
Statement $-1$ is false; Statement $-2$ is true
B
Statement $-1$ is true; Statement $-2$ is true;
Statement $-2$ is not correct explanation for Statement $-1$
C
Statement $-1$ is true; Statement $-2$ is false
D
Statement $-1$ is true; Statement $-2$ is true;
Statement $-2$ is the correct explanation for Statement $-1$
(JEE MAIN-2013)
Solution
| $A$ | $B$ | $ \sim A$ | $A \wedge B$ | ${ \sim A \vee B}$ |
$( {A \wedge B} $ $\to ( { \sim A \vee B}) $ |
$ \sim ( {A \wedge B}) $ $ \to \sim A \vee B ) $ |
| $T$ | $T$ | $F$ | $T$ | $T$ | $T$ | $F$ |
| $T$ | $F$ | $F$ | $F$ | $F$ | $T$ | $F$ |
| $F$ | $T$ | $T$ | $F$ | $T$ | $T$ | $F$ |
| $F$ | $F$ | $T$ | $F$ | $T$ | $T$ | $F$ |
Standard 11
Mathematics
