Say that I have p represent, "Swimming at the NJ shore is allowed;" and say that q represents, "Sharks have been spotted near the shore." If I have the compound proposition [itex]\neg p \rightarrow \neg q[/itex], then it is equivalent to writing [itex]q \rightarrow p[/itex] Yet, that would suggest that the two propositions in English are equivalent. To be precise, "If swimming at the NJ shore is not allowed, then the sharks have not been spotted near the shore." and "If sharks have been spotted near the shore, then swimming at the NJ shore is allowed." Personally, I do not see how these to compound propositions, in English, are remotely equivalent.