Applications and Equivalences
https://slides.com/georgelee/ics141-applications-equivalences/live
What do we use the logics for?
Translating Into English
System Specifications
Sounds pretty boring
http://clientsfromhell.net/
Automated Testing
Where you write code twice
(once as a test case, once to get the test to pass)
Consistent Specifications
A system specification that does not contain any contradictions.
Boolean Searches
Boolean Searches
SQL Queries
SELECT * FROM users
WHERE status = 1
AND (email = 'test@hawaii.edu' OR email = 'admin@hawaii.edu');
Logic Puzzles
Logic Circuits
Tautologies and Contradictions
Tautology
A compound proposition that is always true, no matter what the values of the propositional variables are.
i.e. p v ¬p
Contradiction
A compound proposition that is always false, no matter what the values of the propositional variables are.
i.e. p ^ ¬p
Contingency
A compound proposition that is neither a contradiction nor a tautology (pretty much anything else)
Logical Equivalences
Equivalent
Two expressions that have the same truth values in all cases are logically equivalent.
Or, let p and q be two compound propositions, p and q are logically equivalent if p↔q is a tautology.
Sometimes denoted as ≡
List of Equivalences
There's Too Many!
Refer to Tables 6, 7, 8 on pages 27-28
DeMorgan's Laws
- ¬(p ^ q) ≡ ¬p v ¬q
- ¬(p v q) ≡ ¬p ^ ¬q
Applications and Equivalences
By George Lee
Applications and Equivalences
- 1,201