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Mathematical Reasoning
medium
The statement $(p \Rightarrow q) \vee(p \Rightarrow r)$ is NOT equivalent to.
A
$(p \wedge(\sim r)) \Rightarrow q$
B
$(\sim q) \Rightarrow((\sim r) \vee p)$
C
$p \Rightarrow(q \vee r)$
D
$(p \wedge(\sim q)) \Rightarrow r$
(JEE MAIN-2022)
Solution
$( p \rightarrow q ) \vee( p \rightarrow r )$
$(\sim p \vee q ) \vee(\sim p \vee r )$
$=\sim p \vee( q \vee r )$
$= p \rightarrow( q \vee r ) \equiv(3)$ is true.
$(1)$ $( p \wedge \sim r ) \rightarrow q$
$\sim( p \wedge \sim r ) \vee q =(\sim p \vee r ) \vee q$
$=\sim p \vee( r \vee q )= p \rightarrow( q \vee r )$
$(4)(p \wedge \sim q) \rightarrow r=p \rightarrow(q \vee r)$
Standard 11
Mathematics
