Implications

This week in CSC165 we talked a lot about implications, which can be tricky to wrap your head around.  I try to review the lecture slides after class and test whether I can explain the concepts and/or answer the questions. If not, I look up the topic in the course notes and check the discussion board. It doesn't help that sometimes common language doesn't reflect logic. Consider the idiom:

When it rains, it pours.

The antecedent (P) is "it rains". The consequence (Q) is "it pours". P -> Q. Rain implies pouring but pouring does not imply rain (even though experience tells us it should). The only way to prove this implication false is to find an example of a time when it rained (P is true), but did not pour (Q is false). Therefore, drizzly, gray days are the counter-example that make "when it rain, it pours" false. Perhaps a more logical idiom would be:

When it pours, it rains.

Do you agree or disagree with my logic? Can you think of other idioms that are implications?

The thing I find most tricky about implications is deciding if one statement implies the other, or vice versa. We've gone through some sentences in class as examples and it was only once I heard the answer that it seemed obvious. Before hearing the answer, I could reason either. So I need to get more practice and get comfortable with implications, because they are going to be showing up A LOT.