The negation of the compound statement $^ \sim p \vee \left( {p \vee \left( {^ \sim q} \right)} \right)$ is
$\left( {^ \sim p \wedge q} \right) \wedge p$
$\left( {^ \sim p \wedge q} \right) \vee p$
$\left( {^ \sim p \wedge q} \right){ \vee \,^ \sim }p$
$\left( {^ \sim p{ \wedge ^ \sim }q} \right){ \wedge \,^ \sim }q$
Negation of “Ram is in Class $X$ or Rashmi is in Class $XII$” is
The statement $[(p \wedge q) \rightarrow p] \rightarrow (q \wedge \sim q)$ is
If the inverse of the conditional statement $p \to \left( { \sim q\ \wedge \sim r} \right)$ is false, then the respective truth values of the statements $p, q$ and $r$ is
Which of the following is logically equivalent to $\sim(\sim p \Rightarrow q)$
Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”