Among the two statements

$(S1):$ $( p \Rightarrow q ) \wedge( q \wedge(\sim q ))$ is a contradiction and

$( S 2):( p \wedge q ) \vee((\sim p ) \wedge q ) \vee$

$( p \wedge(\sim q )) \vee((\sim p ) \wedge(\sim q ))$ is a tautology

The proposition $p \Rightarrow \;\sim (p\; \wedge \sim \,q)$ is

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:

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $( p * q ) \odot( p \odot \sim q )$ is a tautology, then the ordered pair $(*, \odot)$ is.

$\left( {p \wedge  \sim q \wedge  \sim r} \right) \vee \left( { \sim p \wedge q \wedge  \sim r} \right) \vee \left( { \sim p \wedge  \sim q \wedge r} \right)$ is equivalent to-