Negation, Converse, or contrapositive?

Question

S: Every employee who is honest and persistent is successful or bored.

Would this statement be the negations, converse, or contrapositive of S?

-> All employees who are dishonest or not persistent must be unsuccessful and not bored.

Answer 1

Sorry if my notation is unfamiliar.

Write \begin{align*} Hx &= \text{$x$ is honest}\\ Px &= \text{$x$ is persistent}\\ Sx &= \text{$x$ is successful}\\ Bx &= \text{$x$ is bored} \end{align*}

Then $S$ can be written $\forall x (Hx \land Px) \to (Sx \lor Bx)$.

The next statement can be written $\forall x (\neg Hx \lor \neg Px) \to (\neg Sx \land \neg Bx)$.

Can you apply De Morgan's laws to make sense of that?

Answer 2

The altered statement is the converse of the contrapositive of $S$.

Contraposive of $S$: "All employees who are unsuccessful and not bored are dishonest or not persistent."

Converse of the contrapositive of $S$: "All employees who are dishonest or not persistent are unsuccessful and not bored."