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Mathematical Reasoning
normal
The negation of the compound statement $^ \sim p \vee \left( {p \vee \left( {^ \sim q} \right)} \right)$ is
A
$\left( {^ \sim p \wedge q} \right) \wedge p$
B
$\left( {^ \sim p \wedge q} \right) \vee p$
C
$\left( {^ \sim p \wedge q} \right){ \vee \,^ \sim }p$
D
$\left( {^ \sim p{ \wedge ^ \sim }q} \right){ \wedge \,^ \sim }q$
Solution
Negative of $\sim p \vee(p \vee(\sim q))$ is
$p \wedge \sim(p \vee \sim q)$
$ \equiv p \wedge \sim q \wedge q$
$\equiv(\sim p \wedge q) \wedge p$
Standard 11
Mathematics
