- Home
- Standard 11
- Mathematics
Mathematical Reasoning
easy
The Boolean expression $( p \Rightarrow q ) \wedge( q \Rightarrow \sim p )$ is equivalent to :
A
$q$
B
$\sim \mathrm{q}$
C
$\mathrm{p}$
D
$\sim \mathrm{p}$
(JEE MAIN-2021)
Solution
$(p \rightarrow q) \wedge(q \rightarrow \sim p)$
$=(\sim P v q) \wedge(\sim q \vee \sim p)\{P \rightarrow q \equiv \sim p \vee q\}$
$\equiv(\sim p \vee q) \wedge(\sim p v \sim q)\{$ commutative property $\}$
$\equiv \sim p \vee(q v \sim q)\{$ distributive property $\}$
$\equiv \sim p$
Standard 11
Mathematics
