Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

*25. THE UNIVERSAL RELATION, TIlE NULL RELATION, AND THE
EXISTENCE OF RELATIONS.
Sumtmary of *25.
This number contains the analogues, for relations, of the definitions and
propositions of *24. Proofs will not be given, as they proceed precisely as
in *24.
The universal relation, denoted by V, is the relation which holds
between any two terms whatever of the appropriate types, whatever these
may be in the given context. The null relation, A, is the relation which
does not hold between any pair of terms whatever, its type being fixed by
the types of the terms concerning which the denial that it holds is significant.
A relation R is said to exist when there is at least one pair of terms between
which it holds; "R exists" is written " t! R."
The propositions of this number are much less often referred to than
those of *24, but for the sake of uniformity we have given the analogues of
all propositions in *24, with the same numeration (except for the integral
part).
All the remarks made in *24 apply, mutatis mutandis, in the present
number.
*25'01. V = (x =. = y) )Df
*25'02. A =- V Df
*25 03. R!. =. (x, y). xRy Df
*25-1.. A v
*25-101. F. =- A
*25-102.: (x, y). (x, y). a y (x, y)= V
25-103. F: (x, y). (, y).: y^ (x, y) = A
*25'104. F. (x, y). xiy
*25'105. F. (x, y). (xAy)
*25-11.. (R).R V
*2512. F.(R).A R

R. & W.

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