Consider the following statements: P: Ramu is intelligent. Q: Ramu...

Given,

$P:$ Ramu is intelligent

$Q:$ Ramu is rich

$R:$ Ramu is not honest

Given statement, "Ramu is intelligent and honest if and only if Ramu is not rich"

$= \left(P ∧ ~ R\right) ⇔ ~ Q$

So, negation of the statement is $~ \left[\left(P ∧ ~ R\right) ⇔ ~ Q\right]$

$= ~ \left[\left\{~ \left(P ∧ ~ R\right) ∨ ~ Q\right\} ∧ \left\{Q ∨ \left(P ∧ ~ R\right)\right\}\right]$

[using $A ⇔ B =$\left(~ A ∨ B\right) ∧ $\left(~ B ∨ A\right)$]

$= \left(\left(P ∧ ~ R\right) ∧ Q\right) ∨ \left(~ Q ∧ \left(~ P ∨ R\right)\right)$

[by using$~ \left(A ∨ B\right) = \left(~ A ∧ ~ B\right)$ and $~ \left(A ∧ B\right) = \left(~ A ∨ ~ B\right)$]