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Mathematical Reasoning
medium
The Boolean Expression $\left( {p\;\wedge \sim q} \right)\;\;\vee \;q\;\;\vee \left( { \sim p\wedge q} \right)$ is equivalent to:
A
$p\;\vee \;q$
B
$\;p\;\vee \; \sim q$
C
$ \sim \;p\; \wedge \;q$
D
$\;p\; \wedge \;q$
(JEE MAIN-2016)
Solution
Consider, $\left( {p \wedge \sim q} \right) \vee q \vee \left( { \sim p \wedge q} \right)$
$\equiv[(p \wedge \sim q) \vee q] \vee(\sim p \wedge q)$
$\equiv[(p \vee \sim q) \wedge t] \vee(\sim p \wedge q)$
$\equiv((p \vee q) \vee(\sim p \wedge q)$
$\equiv(p \vee q \vee \sim p) \wedge(p \vee q \vee q)$
$\equiv(q \vee t) \wedge(p \vee q)$
$\equiv t \wedge(p \vee q)$
$\equiv p \vee q$
Standard 11
Mathematics
