Chapter 9

_REPRESENTATION OF PROPOSITIONS._

§ 1.

_Introductory._

The word "Things" to be henceforwards omitted 27

'=Uniliteral=' Proposition "

'=Biliteral=' do. "

Proposition '=in terms of=' certain Letters "

§ 2.

_Representation of Propositions of Existence._

The Proposition "Some x exist" 28

Three other similar Propositions "

The Proposition "No x exist" "

Three other similar Propositions 29

The Proposition "Some xy exist" "

Three other similar Propositions "

The Proposition "No xy exist" "

Three other similar Propositions "

The Proposition "No x exist" is _Double_, and is equivalent to the two Propositions "No xy exist" and "No xy' exist" 30

pg-xxi § 3.

_Representation of Propositions of Relations._

The Proposition "Some x are y" "

Three other similar Propositions "

The Proposition "Some y are x" 31

Three other similar Propositions "

Trio of equivalent Propositions, viz. "Some xy exist" = "Some x are y" = "Some y are x" "

'=Converse=' Propositions, and '=Conversion=' "

Three other similar Trios 32

The Proposition "No x are y" "

Three other similar Propositions "

The Proposition "No y are x" "

Three other similar Propositions "

Trio of equivalent Propositions, viz. "No xy exist" = "No x are y" = "No y are x" 33

Three other similar Trios "

The Proposition "All x are y" is _Double_, and is equivalent to the two Propositions "Some x are y" and "No x are _y'_" "

Seven other similar Propositions 34

=Tables II, III.= Representation of Propositions of Existence and Relation 34, 35