Truth tables are a simple way to analyze a system of statements to determine if they are always
consistent (Tautology), always inconsistent (Contradiction), or are conditionally consistent and
require more detailed analysis. But even though any given statement can only take on two
values, True or False, a system of n statements takes on 2
possible values. This exponential
growth makes it impractical to use only truth tables to “solve” logic problems. But just as the
rules of Algebra can be used to simplify a complicated math problem by combining like terms or
cancelling common factors, so to can logical equivalences be used to reduce a very large
potential space into something that is more manageable.
In this Project you will construct a Truth Table for a larger but still relatively small system of
statements to show that a compound statement is a Tautology. Then you will repeat the proof
using only logical equivalences, being sure to include and explain all steps in your process. If
you do any external research be sure to properly cite your sources. If you work with another
student(s), please include their name(s) in the write-up as well. If you use any electronic
resources, be sure to name them in the report).
Use a Truth Table to show that “(𝑝∨𝑞)∧(¬𝑝∨𝑟)→(𝑞∨𝑟)”is a Tautology. Then show it using only
Logical Equivalences. (Hint: Associative Laws.)
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