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Mathematical Reasoning
hard
The statement $(p \wedge(\sim q) \vee((\sim p) \wedge q) \vee((\sim p) \wedge(\sim q))$ is equivalent to
A
$(\sim p) \vee(\sim q)$
B
$p \vee(\sim q)$
C
$(\sim p) \vee q$
D
$p \vee q$
(JEE MAIN-2023)
Solution
$(p \wedge(\sim q) \vee((\sim p) \wedge q) \vee((\sim p) \wedge(\sim q))$
$\left(p^{\wedge}(\sim q)\right) \vee\left((\sim p)^{\wedge}(q \vee(\sim q))\right)$
$\left(p^{\wedge}(\sim q)\right) \vee\left((\sim p)^{\wedge} t\right)$
$\left(p^{\wedge}(\sim q)\right) \vee(\sim p)$
$(\sim p) \vee\left(p^{\wedge} \sim q\right)$
$(\sim p \vee p)^{\wedge}(\sim p \vee \sim q)$
$t^{\wedge}(\sim p \vee \sim q)$
$=\sim p \vee \sim q$
Standard 11
Mathematics
