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Mathematical Reasoning
medium
The statement $A \rightarrow( B \rightarrow A )$ is equivalent to
A
$A \rightarrow( A \wedge B )$
B
$A \rightarrow( A \rightarrow B )$
C
$A \rightarrow( A \leftrightarrow B )$
D
$A \rightarrow(A \vee B)$
(JEE MAIN-2021)
Solution
$A \rightarrow( B \rightarrow A )$
$\equiv A \rightarrow(\sim B \vee A )$
$\equiv \sim A \vee(\sim B \vee A )$
$\equiv(\sim A \vee A ) \vee \sim B$
$\equiv T \vee \sim B \equiv T$
$\therefore T \vee B = T$
$\equiv(\sim A \vee A ) \vee B$
$\equiv \sim A \vee( A \vee B )$
$\equiv A \rightarrow( A \vee B )$
Standard 11
Mathematics
