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

and

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.

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Section 1.2: Problem 15 Solution

Section 1.2: Problem 15 Solution