How to prove a set of propositional connectives is NOT adequate?

[philoss]

I know how to prove if a set is adequate (all the main conncectives can be made from the set), but how would you prove that it is impossible to make all the connectives using this set?
For instance how would you prove if a set of connectives {and, or} is NOT adequate?

This is a question I thought of for preperation for a exam.

Any answer is appreciated.

Thanks

 

[EnumaElish]

Perhaps this might help: http://www.math.uwaterloo.ca/~snburris/htdocs/LOGIC/ST_ALGORS/st_adeq.html

 

[EnumaElish]

Note that on the site I posted, K = "NOT 2nd" and M = "NOT 1st."

Also from http://en.wikipedia.org/wiki/Functional_completeness#Informal I surmise that {and, or} is not adequate because the "NOT" operator, which is excluded from the set, is necessary for generating the "--->" (if/then; implies) relationship.

 

[Math Is Hard]

Note: moved this thread from Philosophy. This will likely be a better place to get help with this type of question.

 

[EnumaElish]

I agree; I guess there is a difference between propositional logic and "philosophical" logic, and sometimes it gets ignored.