c. Let p : You earn a bachelor's degree. Let q : Your income potential increase. Given the statement "If you earn a bachelor's degree, then your income potential increases." The negation of the conditional statement is \( \left.\qquad \begin{array}{l}O(p \rightarrow q) \\ O \\ \sim(p \rightarrow \sim q) \\ O(\sim p \rightarrow \sim q) \\ \end{array}\right) \sim(\sim p \rightarrow q) \)

To negate the conditional statement "If you earn a bachelor's degree, then your income potential increases," we need to reframe it. The original statement can be expressed as \( p \rightarrow q \), which means if p is true, then q is also true. The negation involves stating that it is possible for p to be true while q is false, leading us to \( p \land \sim q \). Therefore, the correct negation of the original statement is not among the options provided but can be interpreted as "You earn a bachelor's degree and your income potential does not increase." In terms of logic, a conditional statement can be tricky, but understanding how it works opens doors to logical reasoning. When you encounter "if-then" scenarios, remember that the only time the conditional fails is when the first part is true but the second part is false. This common point of confusion often leads to misunderstandings in both academic settings and everyday decisions, so keep an eye out!