I remember when I took Dr. Marr's graph labeling class, we talked about how iff statements need to be proved in both directions. That now makes more sense when I see the symbol (double pointing arrow) used to denote "p if and only if q".

This answers my question from the previous section!

Is it possible to do one of these on more than 2 propositions at a time (like maybe 3)?

This reminds me of when using '&&' for an if condition, both values must be true for the overall value to be true. I think it is interesting to see how different subjects (computer science and mathematics) represent the same idea. Moreover, I find it interesting that the symbols used are different as well.

Are there any special cases where a proposition can be true then false, or false then true? Or will a proposition always be either true or false?