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### If then statement regrading definition of lognormal distribution and the inverse of that statement?

Hello I'm learning about probability distributions and this was the given definition for a lognormal distribution: A random variable X follows a lognormal distribution if its natural logarithm, ln ...
In a definition like the following: An object $x$ is called $P$ if [and only if] it has properties $p$ and $q.$ should one use an implication (if) or an equivalence (if and only if)? It makes ...
In one of the works about tree languages I met the following definition: Let $\mathcal{N}$ be the set of nonnegative integers and let $U$ be the free monoid generated by $\mathcal{N}$ with ...