# Section 2.6: Problem 5 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

Find prenex formulas equivalent to the following.

(a)
.

(b)
.

(a) The following transformations are based on tautological equivalence, and the EAV and Prenex Normal Form theorems.

(b) The following transformations are based on tautological equivalence, and the EAV and Prenex Normal Form theorems.

Note. In both cases it might be easier to get the answer by considering when the sentence is false. (a) is false when the following is true,
,
,
,
,
. (b) is false when the following is true,
or
,
or
,
or
,
or
,
or
.