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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 n possible values. This exponential growth makes it impractical to use only truth tables to β€œsolve” 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 β€œ(π‘βˆ¨π‘ž)∧(Β¬π‘βˆ¨π‘Ÿ)β†’(π‘žβˆ¨π‘Ÿ)”is a Tautology. Then show it using only Logical Equivalences. (Hint: Associative Laws.)

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Mini Discrete Math Project Involving Logical Equivalences
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