# Section 1.2: Problem 15 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
Of the following three formulas, which tautologically imply which?
(a)
(b)
(c)
(a) is evaluated to iff and are both assigned or both assigned . (b) is iff is false iff is and is iff both and are iff and are both assigned or both assigned . (c) is iff both and are true iff either is true then is false and is true, or is false then is true and is false iff and are both assigned or both assigned . Therefore, all three formulas are tautologically equivalent.