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  • Negation of the statement is :Option: 1 <img alt="\sim \mathrm{p} \wedge \mathrm{q} \we

Negation of the statement (p \vee r) \Rightarrow(q \vee r) is :
Option: 1 \sim \mathrm{p} \wedge \mathrm{q} \wedge \sim \mathrm{r}
Option: 2 \sim \mathrm{p} \wedge \mathrm{q} \wedge \mathrm{r}
Option: 3 \mathrm{p} \wedge \sim \mathrm{q} \wedge \sim \mathrm{r}
Option: 4 \mathrm{p} \wedge \mathrm{q} \wedge \mathrm{r}

Answers (1)

best_answer

p\Rightarrow q\\ is equivalent to \sim p \vee q

So  \sim\left ( p\Rightarrow q \right )\equiv \left ( p\wedge\sim q \right )\\

\Rightarrow \sim((p \vee r) \Rightarrow(q \vee r)) \equiv(p \vee r) \wedge\sim\left ( q \vee r \right ) \\

\equiv (p \vee r) \wedge(\sim q \wedge \sim r) \\

\equiv ((p \vee r) \wedge(\sim r)) \wedge \sim q \\

\equiv (p \wedge \sim r) \vee(r \wedge \sim r) \wedge \sim q

\equiv p\wedge \sim r\wedge\sim q

Posted by

Kuldeep Maurya

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