Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following:

Consider the two statements :

$(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology

$(S2): (\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$ is a fallacy.

Then :

The following statement $\left( {p \to q} \right) \to $ $[(\sim p\rightarrow q) \rightarrow  q ]$ is

The proposition $p \rightarrow \sim( p \wedge \sim q )$ is equivalent to

Statement $\quad(P \Rightarrow Q) \wedge(R \Rightarrow Q)$ is logically equivalent to

Let $r \in\{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee(\sim p) \Rightarrow(p \wedge q) \vee r \quad$ is a tautology. Then ' $r$ ' is equal to