Consider the following three statements :
$P : 5$ is a prime number.
$Q : 7$ is a factor of $192$.
$R : L.C.M.$ of $5$ and $7$ is $35$.
Then the truth value of which one of the following statements is true?

Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is

The Boolean expression $ \sim \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ 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 equivalently expressed as

Negation of the Boolean statement $( p \vee q ) \Rightarrow((\sim r ) \vee p )$ is equivalent to

Consider the following statements:

$P :$ Ramu is intelligent

$Q $: Ramu is rich

$R:$ Ramu is not honest

The negation of the statement "Ramu is intelligent and honest if and only if Ramu is not rich" can be expressed as.