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

442~

RELATION-ARITHMETIC

[PART IV

*172-43. F: Tr Q C'CCQeLPsmor sinor Q.).
(T /ICnv'Tt-) C 4HI& e rITP)smo~o (R'Q)
[*172~42442 1]
*172-44. F P smor smor Q... H'P sinor II'Q [*172-42]
*172-45. F:.Multax. ):P,QeRel12excl. a! P smor Q n Rl'smor.).
1241JP smor H1'Q
[*16444.*17244]
The following proposition shows that if two relations have the same field,
and if the parts of them that are contained in diversity are the same, they
have the same product. Thus e.g. Hl'P,, = EI'P*, in virtue of *91-541.
*172-5. F-:C'P=O'Q.PA J=QtNJ.).ll'P=1J'Q
Dern.
F. *50-11.F:. Hp.): RPS. R S.. RQS. R #S (1)
F. (1). *172-11. F. Prop
The following proposition is used in *182-42.
*17251. F. fl'P = '(P v I r C'P) [*172-5]
*172-52. FQ:.Qe C['P. )Q.QjtR). RPQ. R t Q: D. fl'P= H'(P r% J)
Dern.
F.*50-11. ) F: Hp. ).CUP C CI(P tJ) (1)
F. *3:314. *9:3-101. Transp. D F-: QPQ. ). Q r eB'P:
[Transp.*331:3] D)1-: Q c B'P. D.(gR). QPR. Rt Q.
[*5011] )QG'6(PAJ) (2)
F.(1).(2). *93-103. D)F: Hp..C'P C C(P i- J).
[*33265] ). C'P = C'(P il J) (3)
F.(3). *172-5. )F. Prop
Thus we shall always have flP = Hll(P A~ J) unless there are members of
(IIP which have no referent except themselves.