Propositional Logic

Abstract

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• Deals with the logic of Mathematical Statement

Ambiguous

• Happen without the proper use of parentheses to indicate the intended order of operations
• We need to use proper parentheses to ensure there’s only one way to interpret and evaluate each expression

Logical Connectives

• Negation: NOT performed first
• Disjunction: OR ,Conjunction: AND coequal, make sure proper parentheses is used to avoid Ambiguous
• If-then/implies: performed last, coequal with iff

Logical Equivalence

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• The above is Theorem 2.1.1
• We have a logical equivalence when 2 Mathematical Statement have identical truth values
• The above diagram shows Logical Equivalence Laws that can used to simplify mathematical statement

Usage of Laws

We can only perform the laws when the exact form is matched

2 ways to check for logical equivalence

1. Truth table - Find a row where truth values are different
2. Find a counter example - Substitute a concrete Mathematical Statement, then compare