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 \[ \sim(p \rightarrow q) \] \( \sim(p \rightarrow \sim q) \) \( \sim(\sim p \rightarrow \sim q) \) \( \sim(\sim p \rightarrow q) \)

To tackle this delightful logic puzzle, let's first clarify what the conditional statement \( p \rightarrow q \) means. It translates to "If \( p \) (you earn a bachelor's degree) is true, then \( q \) (your income potential increases) is also true." The negation of this statement means that you can earn a bachelor's degree without an increase in income potential. Therefore, the correct negation is represented as \( \sim(p \rightarrow q) \). This equates to the situation where you earn the degree (p is true) but don't see the income increase (q is false). Now, let’s stir things up a bit! To find the correct negation based on options, we're looking for when \( p \) is true and \( q \) is false. In logical terms, that means we want \( \sim p \vee q \) to be false, which leads us back to our main point: \( p \) holds yet \( q \) does not. So, if you're diving into this logical conundrum, embracing that \( \sim(p \rightarrow q) \) is the key to unlocking the challenge!