[pg071]CHAPTER II.
REPRESENTATION OF PROPOSITIONS OF RELATION.
Let us take, first, the Proposition “Some x are y”.
This, we know, is equivalent to the Proposition of Existence “Some xy exist”. (See [p. 31].) Hence it may be represented by the expression “xy1”.
The Converse Proposition “Some y are x” may of course be represented by the same expression, viz. “xy1”.
Similarly we may represent the three similar Pairs of Converse Propositions, viz.—
“Some x are y′” = “Some y′ are x”,
“Some x′ are y” = “Some y are x′”,
“Some x′ are y′” = “Some y′ are x′”.
Let us take, next, the Proposition “No x are y”.
This, we know, is equivalent to the Proposition of Existence “No xy exist”. (See [p. 33].) Hence it may be represented by the expression “xy0”.
The Converse Proposition “No y are x” may of course be represented by the same expression, viz. “xy0”.