Section 2.2: Problem 1 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
Show that (a)
iff
; and (b)
,
iff
.
(a)
iff for every structure
and
,
implies
iff for every structure
and
,
implies if
then
iff for every structure
and
,
implies
iff
.
(b)
,
iff (using (a))
,
iff for every structure
and
,
iff for every structure
and
,
iff
.