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Mathematical Reasoning
easy
Negation of the statement $(p \vee r) \Rightarrow(q \vee r)$ is :
A
$\mathrm{p} \wedge \sim \mathrm{q} \wedge \sim \mathrm{r}$
B
$\sim \mathrm{p} \wedge \mathrm{q} \wedge \sim \mathrm{r}$
C
$\sim \mathrm{p} \wedge \mathrm{q} \wedge \mathrm{r}$
D
$\mathrm{p} \wedge \mathrm{q} \wedge \mathrm{r}$
(JEE MAIN-2021)
Solution
$\because \sim(\mathrm{A} \Rightarrow \mathrm{B})=\mathrm{A} \wedge \sim \mathrm{B}$
$\therefore \sim((\mathrm{p} \vee \mathrm{r}) \Rightarrow(\mathrm{q} \vee \mathrm{r}))$
$=(\mathrm{p} \vee \mathrm{r}) \wedge(\sim \mathrm{q} \wedge \sim \mathrm{r})$
$=((\mathrm{p} \vee \mathrm{r}) \wedge(\sim \mathrm{r})) \wedge(\sim \mathrm{q})$
$=\mathrm{p} \wedge(\sim \mathrm{r}) \wedge(\sim \mathrm{q})$
Standard 11
Mathematics
