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

1. Jun 9, 2010

### 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.

Thanks

2. Jun 11, 2010

### EnumaElish

3. Jun 12, 2010

### 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.

Last edited: Jun 13, 2010
4. Jun 13, 2010

### Math Is Hard

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

5. Jun 13, 2010

### EnumaElish

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