Negation of statement (( A wedge( B vee C )) ⇒( A vee B )) ⇒ A is

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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

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