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Mathematical Reasoning
medium
बुलीयन कथन $(p \vee q) \Rightarrow((\sim r) \vee p)$ का निपेध किस के समतुल्य है :
A
$p \wedge(\sim q ) \wedge r$
B
$(\sim p ) \wedge(\sim q ) \wedge r$
C
$(\sim p ) \wedge q \wedge r$
D
$p \wedge q \wedge(\sim r )$
(JEE MAIN-2022)
Solution
$P \vee q \Rightarrow(\sim r \vee p )$
$\equiv \sim( p \vee q ) \vee(\sim r \vee p )$
$\equiv(\sim p \wedge \sim q ) \vee( p \vee \sim r )$
$\equiv[\sim p \vee p) \wedge(\sim q \vee p)] \vee \sim r$
$\equiv[\sim q \vee p) \vee \sim r$
Its negation is $\sim p \wedge q \wedge r$
Standard 11
Mathematics
