Negation of the conditional : “If it rains, I shall go to school” 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:

Consider the following statements 

$P :$ Suman is brilliant

$Q :$ Suman is rich

$R :$ Suman is honest

The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as 

If $p, q, r$ are simple propositions with truth values $T, F, T$, then the truth value of $(\sim p \vee q)\; \wedge \sim r \Rightarrow p$ is

The statement $A \rightarrow( B \rightarrow A )$ is equivalent to

The Boolean expression $\sim\left( {p\; \vee q} \right) \vee \left( {\sim p \wedge q} \right)$ is equivalent ot :