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Mathematical Reasoning
hard
The negation of the statement $(( A \wedge( B \vee C )) \Rightarrow( A \vee B )) \Rightarrow A$ is
A
equivalent to $\sim A$
B
equivalent to $\sim C$
C
equivalent to $B \vee \sim C$
D
a fallacy
(JEE MAIN-2023)
Solution
$p :(( A \wedge( B \vee C )) \Rightarrow( A \vee B )) \Rightarrow A$
${[\sim( A \wedge( B \vee C )) \vee( A \vee B )] \Rightarrow A }$
${[( A \wedge( B \vee C )) \wedge \sim( A \vee B )] \vee A }$
$( f \vee A )= A$
$\sim p \equiv \sim A$
Standard 11
Mathematics
