# Section 2.1: Problem 3 Solution

Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James R. Munkres

In 3–8, translate each English sentence into the first-order language specified. (You may want to carry out the translation in several steps, as in some of the examples.) Make full use of the notational conventions and abbreviations to make the end result as readable as possible.

Neither
nor
is a member of every set. (
, for all sets;
, is a member of;
,
;
,
.)

English sentence “neither
nor
is
” means literally “
is not
, and
is not
”, hence,
, or, alternatively,
(but this latter sentence is a translation of a slightly different, though “logically equivalent”, English sentence “there is a set such that
is not a member of it, and there is a set such that
is not a member of it”).