Abstract
- 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:
NOTperformed first - Disjunction:
OR, Conjunction:ANDcoequal, 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
Important
The above diagram shows Logical Equivalence Laws that can used to simplify mathematical statement.
2 ways to check for logical equivalence
- Truth table - Find a row where truth values are different
- Find a counter example - Substitute a concrete Mathematical Statement, then compare
Usage of Laws
We can only perform the laws when the exact form is matched.