Which of the following is always true
$(p \Rightarrow q) \equiv \;\sim q \Rightarrow \;\sim p$
$\sim (p \vee q) \equiv \vee \;p\; \vee \sim q$
$\sim (p \Rightarrow q) \equiv p\; \wedge \sim q$
$\sim (p \vee q) \equiv \;\sim p\;\; \wedge \sim q$
Let $r \in\{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee(\sim p) \Rightarrow(p \wedge q) \vee r \quad$ is a tautology. Then ' $r$ ' is equal to
The negation of the statement
''If I become a teacher, then I will open a school'', is
When does the current flow through the following circuit
If $\mathrm{p} \rightarrow(\mathrm{p} \wedge-\mathrm{q})$ is false, then the truth values of $p$ and $q$ are respectively
The negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to