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If, as before, L means inclusion and N exclusion, then 
L + N= 0, 
that is to say, these relations are contradictory. 
Relatives are either invertible or uninvertible, and either 
transitive or intransitive. Using L as the symbol of relation 
generally, the symbol of invertibleness is 
L~ l = L, 
and the symbol of transitiveness is 
Z 2 = A 
There are thus four classes of relations. 
1. Transitive and invertible. To this class belong the 
relations of identity, and similarity in any one respect. 
The only numerical coefficient that combines these proper- 
ties is unity. 
2. Transitive and uninvertible. To this class belongs, 
among others, the relation of inclusion. The only numerical 
coefficients that combine these properties are zero and 
infinity. 
3. Intransitive and invertible. To this class belongs, 
among others, the relation of exclusion. The only numerical 
coefficient that combines these properties is negative unity. 
4. Intransitive and uninvertible. To this class belong an 
infinite variety of relations : — among others, partial inclusion 
(some A is B). These properties are combined in all 
numerical coefficients except unity, negative unity, zero, 
and infinity. 
