# Section 2.4: Problem 2 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

To which axiom groups, if any, do each of the following formulas belong?

(a)
.

(b)
.

(c)
.

(a) The formula is valid and has the form of
which is a tautology, group 1.

(b) The formula is a generalization of
and has the form of
where
is substitutable for
in
, group 2.

(c) This is not a valid formula, consider, for example,
.