c. Let \( p: \) I am in Califomia. Let \( q: \) I am in Napa Valley. Given the statement "I am not in California, then I am not in Napa Valley." The negation of the conditional statement is \( O \sim(\sim q \rightarrow \sim p) \) \( O \sim(\sim p \rightarrow \sim q) \) \( O \sim(p \rightarrow \sim q) \) \( O \sim(\sim p \rightarrow q) \)

To find the negation of the conditional statement "If I am not in California, then I am not in Napa Valley," we start by recognizing the structure of the statement: \(\sim p \rightarrow \sim q\). The negation of a conditional statement \(R \rightarrow S\) is given by \(R \land \sim S\). In this case, that means the negation is \(\sim(\sim p \rightarrow \sim q) = \sim(\sim p) \land \sim(\sim q) = p \land q\). Translating this back into our context, the negation is essentially asserting that "I am in California and I am in Napa Valley." Understanding such logical structures can help one navigate various fields, such as computer programming or law, where clear and precise statements are crucial. Using these concepts, you can fluidly interpret and manipulate conditions in a variety of practical situations, from coding algorithms to drafting legal arguments! If you'd like to further explore the world of logic and contradictions, delve into the realm of syllogisms or even explore modern logic puzzles, which often showcase this type of reasoning in sometimes humorous or perplexing ways!