Originally Posted by

**Doktor_Faustus** Hi guys,

Just to continue this discussion about if/then:

I've managed to confuse myself again, but I was thinking about the statement (1) " if it rains, then there are clouds."

If the premise is true and the conclusion is false, then the implication is false - If it's raining, there must be clouds.

If the premise is false and the conclusion is true, then the implication is true - it may be cloudy, but that does not mean that it is raining.

If the premise is false and the conclusion is false, then the implication is true - No rain, no clouds.

Makes sense.

Then I thought about it another way.

(2) "If there are clouds, then it is raining. "

what I'm confused about is this: Lets say the premise in (2) is false, but the conclusion is true. According to the truth table, the implication is true. However, as far as I know, there can't be rain without clouds.

I know I'm missing something. Anyone mind clarifying this for me ? Does it just mean that the assumption - or premise - is incorrect ? That is, if it's raining, then there must be clouds, and anyone who says there are no clouds is lying ?

Cheers.