# 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 .