The statement $( p \rightarrow( q \rightarrow p )) \rightarrow( p \rightarrow( p \vee q ))$ is

If the Boolean expression $( p \wedge q ) \circledast( p \otimes q )$ is a tautology, then $\circledast$ and $\otimes$ are respectively given by

The proposition $ \sim \left( {p\,\vee \sim q} \right) \vee  \sim \left( {p\, \vee q} \right)$ is logically equivalent to

$\sim (p \vee q) \vee (\sim p \wedge q)$ is logically equivalent to

Consider the following statements:

$P$ : I have fever

$Q:$ I will not take medicine

$R$ : I will take rest

The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:

$p \Rightarrow q$ can also be written as