• 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

  • 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