Are you rich?

"If you are happy, then you are rich. So, are you happy? If yes, I conclude that you are rich."

Or should I say,

"If you are rich, then you are happy.
So, are you happy? If not, I conclude that you are poor." (Poor you.)

Or is it rather the case that,

"You are rich if and only if you are happy"?

Now, if you are moneyed, are you rich? Well, that depends on your meaning of being rich.