Negation is $“2 + 3 = 5$ and $8 < 10”$ is

For the statements $p$ and $q$, consider the following compound statements :

$(a)$ $(\sim q \wedge( p \rightarrow q )) \rightarrow \sim p$

$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$

Then which of the following statements is correct?

$\sim p \wedge q$ is logically equivalent to

Let $p , q , r$ be three logical statements. Consider the compound statements $S _{1}:((\sim p ) \vee q ) \vee((\sim p ) \vee r ) \text { and }$ and $S _{2}: p \rightarrow( q \vee r )$ Then, which of the following is NOT true$?$

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.

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