3-adic relation. The 
problem with this is that a 3-adic relation requires EXACTLY
3 components, not at least 3 components, and that these three
components are necessary for identity.

Relatively few things in real life meet the criterion of exactly
3 components, and though I agree that the example you have used 
of logical operators is one of them, activities generally are not. 
However, even with logical operators it is possible to represent 
these without using 3-adic relations, although I agree that thi