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  4. The statement A arrow( B arrow A ) is equivalent to

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Q. The statement $A \rightarrow( B \rightarrow A )$ is equivalent to

JEE MainJEE Main 2021Mathematical Reasoning

Solution:

$A \rightarrow( B \to A )$
$\equiv A \to(\sim B \vee A )$
$\equiv \sim A \vee(\sim B \vee A )$
$\equiv(\sim A \vee A ) \vee \sim B$
$\equiv T \vee \sim B \equiv T$
$\therefore T \vee B = T$
$\equiv(\sim A \vee A ) \vee B$
$\equiv \sim A \vee( A \vee B )$
$\equiv A \to( A \vee B )$