If $(p \wedge \sim q) \wedge r  \to \sim r$ is $F$ then truth value of $'r'$ is :-

The negation of $ \sim s \vee \left( { \sim r \wedge s} \right)$ is equivalent to :

Let $p$ and $q$ denote the following statements
$p$ : The sun is shining
$q$ : I shall play tennis in the afternoon

The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is 

The Boolean expression $ \sim \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ is equivalent to

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?

The conditional $(p \wedge q) ==> p$ is