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:

Step-by-step solution

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" = P ∧ ~ R ⇔ ~ Q So, negation of the statement is ~ P ∧ ~ R ⇔ ~ Q = ~ ~ P ∧ ~ R ∨ ~ Q ∧ Q ∨ P ∧ ~ R [using A ⇔ B = ~ A ∨ B ∧ ~ B ∨ A ] = P ∧ ~ R ∧ Q ∨ ~ Q ∧ ~ P ∨ R [by using ~ A ∨ B = ~ A ∧ ~ B and ~ A ∧ B = ~ A ∨ ~ B ]