Let $p , q , r$ be three statements such that the truth value of $( p \wedge q ) \rightarrow(\sim q \vee r )$ is $F$. Then the truth values of $p , q , r$ are respectively

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

The compound statement $(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) \Rightarrow((\sim P ) \wedge(\sim Q ))$ 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?

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 statement $(p \Rightarrow q) \vee(p \Rightarrow r)$ is NOT equivalent to.