Introduction to Logic by Gensler Harry J

Author:Gensler, Harry J. [Gensler, Harry J.]
Language: eng
Format: mobi, epub, pdf
Publisher: Taylor and Francis
Published: 2010-05-25T23:00:00+00:00

At least two are rich =

= For some x and some y: x≠y, x is rich, and y is rich.

(∃x)(∃y)(∼x=y · (Rx · Ry))

The pair of quantifiers “(∃x)(∃y)” (“for some x and some y”) doesn’t say whether x and y are identical; so we need “∼x=y” to say that they aren’t.

Henceforth we’ll often need more variable letters than just “x” to keep references straight. It doesn’t matter what letters we use; these two are equivalent:

(∃x)Rx

(∃y)Ry =

= At least one being is rich.

At least one being is rich.

Here’s how we translate “exactly one” and “exactly two”:

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