Propositional Logic Flashcards
What is a proposition?
An atom of knowledge - an inseparable unit of knowledge
What are key properties of propositions?
- Captures meaning
- Supports reasoning methods
- Each symbol can be either true or false
What is an example of a proposition?
A bike has two wheels
What is an example of something that is not a proposition?
Are you going to the lecture?
What does the backwards arrow represent in propositional logic?
NOT
What does ∧ represent in propositional logic?
AND
What does ∨ represent in propositional logic?
OR
What does ⇒ represent in propositional logic?
Implies.
P ⇒ Q means: “if P is true, then Q is true, otherwise I am making no claim.”
What does ⇔ represent in propositional logic?
Equivalence.
What is the order of precedence in propositional logic?
Not
And
Or
Implies
Equivalence
What is the associativity of AND rule?
((P ∧ Q) ∧ R)
is equivalent to
(P ∧ (Q ∧ R))
What is the associativity of OR rule?
((P ∨ Q) ∨ R)
Is equivalent to
(P ∨ (Q ∨ R))
What is the contraposition rule?
(P ⇒ Q)
is equivalent to
(¬Q ⇒ ¬P)
What is the rule of implication elimination?
(P ⇒ Q)
is equivalent to
(¬P ∨ Q)
What is the rule of biconditional elimination?
(P ⇔ Q)
is equivalent to
((P ⇒ Q) ∧ (Q ⇒ P))
