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

SECTION D] CLASSES OF MUTUALLY EXCLUSIVE CLASSES

541

We have next (*84'2 —28) a set of propositions dealing with various
special cases, such as A and 1. The most useful of these are
*84-23.. t'ca e Cls2 excl
*84-241. F. iCa e Cls ex2 excl
*84-25. bF: K e Cls2 excl. X C c. ). X e Cls2 excl
We next have a set of propositions (*84'3 —37) which are immediate
consequences of propositions in *81, by means of *84'14. The most useful
of these is
*84-3. F: K e Cls2 excl. ). ea/'c C 1 - 1
We next have a set of propositions (*84'4 —43) dealing with the
domains of selections from a Cls2 excl. These are for the most part still
immediate consequences of propositions in *81, in virtue of *84'14. The
most useful are
*84-41. F: e e Cls2 excl. D. D,e1'C e 1 1. D"e'c sm ea^'
*84'412. F: Ke Cls2 excl.. D"e c K= / {Le Kc.. aL rn a e: ~ C s'C}
*84-43.:. a, /3 Cls2 excl. s'a = s'/3.: a CD"e'/3. -. C D"a'
This proposition applies to such cases as the relations of rows and
columns. Imagine any set of terms arranged in rows and columns so as
to form a rectangle. Then each column is a selection from the rows, and
each row is a selection from the columns. This is a particular case of the
above proposition.
We next have a set of propositions on R/c, R' ", and P^"K (*84'5-'55).
The most important of these are
*84-51. F: R r K Cls -1.). R"K CIs2 excl
*84-53. F: R e Cls - 1. E e Cls2 excl. D. R"gK e Cls2 excl
Finally we have a set of propositions (*84'59-'62) showing circumstances
under which K V X is a Cls2excl. The only one of these which is used
subsequently is
*84-62. F:a. a 4 /3. ): 'a u 3 e Cls2 excl. = a n B3 = A
*84-01. Cls2excl==E(a, /3eK. a(8.),,a.anI3=A) Df
*84-02. Cl excl'y = Cls2 excl n Cl'y Df
4 -*84-03. Cls ex2 excl = Cls2 excl - e 'A Df
*841. F:. K e Cls" excl. -: a, 3 e Kc. a 3. D1,3. a n / = A
[*203. (*84-01)]