FIT2014 Lecture Notes - Lecture 2: First-Order Logic, Qi
28 Jun 2018
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Lecture 2: Proposition Logic
Proposition
Proposition is a statement which is either true or False
2+2 = 4: is a proposition which is true.
The moon is made of cheese: is proposition which is false
It will rain tomorrow is a proposition
This statement is false is not a proposition
Vote for Mickey Mouse is not a proposition.
Negation
P: I have three children
¬P: I do not have three children
Other Notation: ~P, P
Connectives
Predicate logic:
- And ∧ (&)
- Or ∨
- Implies ⇒ (→)
- Equivalence ⇔ (↔)
Conjunction
P: This subject is interesting
Q I am tired
P^Q:
This subject is interesting and I am tired
This subject is interesting although I am tired
This subject is interesting but I am tired
Disjunction: (it is inclusive)
P: Sue is a football player
Q: Bob is lazy
P ∨ Q: Sue is a football player or Bob is lazy
De Morgan’s Law
¬ (P ∨ Q) = ¬P ∧ ¬Q ¬ (P ∧ Q) = ¬P ∨ ¬Q
Document Summary
Proposition is a statement which is either true or false. 2+2 = 4: is a proposition which is true. The moon is made of cheese: is proposition which is false. This statement is false is not a proposition. Vote for mickey mouse is not a proposition. This subject is interesting and i am tired. This subject is interesting although i am tired. This subject is interesting but i am tired. P (cid:1513) q: sue is a football player or bob is lazy. (p (cid:1513) q) = p (cid:1512) q. (p (cid:1512) q) = p (cid:1513) q. If it is tuesday, then we are in belgium. It is being tuesday implies we are in belgium. It is tuesday only if we are in belgium. It is being tuesday is sufficient for us to be in belgium. The world will blow up if and only if kaos rules the world.
