Natural language and symbols

As we learn about symbolic notation, I'm finding it really interesting to think about how I communicate in english.

A really interesting word was "unless." X unless B translates to X if not B, according to the slides.
if (not X):
B

"Unless you can pay, don't touch that" would translate to the following:
if (not ableToPay):
do not touch

I think that making conversions like this really helps my understanding of what these different words mean, and how to interpret natural language sentences into precise "math language."

Another interesting set of words are "and" and "or." Let's do some more natural language conversions!
- I am part of math club AND science club
=> I am (part of math club) AND (part of science club)

But what about the following:
- Members of the math club and the science club can attend the fair.
So in this case, converting it to symbolic notation with an "and" would not be true to the intended meaning. In actuality, one would use an "or" in order to be precise, since the statement is attempting to say that both clubs' members can come. I wonder if our normal english language use should adapt to this precision.