# 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.