I. Logic and Proof
1. Propositional Logic
A proposition is a declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both.
Name | Meaning | Notation |
---|---|---|
negation | not p | |
disjunction | p or q | |
conjunction | p and q | |
conditional | if p, then q | |
biconditional | p if and only if q |
2. Propositional Equivalences
A compound proposition that is always true, no matter what the truth values of the propositional variables that occur in it, is called a tautology.
A compound proposition that is always false is called a contradiction.
A compound proposition that is neither a tautology nor a contradiction is called a contingency.
The compound propositions p and q are called logically equivalent if is a tautology. (
)
Equivalence | Name |
---|---|
Identity laws | |
Domination laws | |
Idempotent laws | |
Double negation law | |
Commutative laws | |
Associative laws | |
Distributive laws | |
De Morgan’s laws | |
Absorption laws | |
Negation laws | |
Table of common Logical equivalence |
3. Predicates and Quantifiers
To be done
References
Discrete Mathematics and Its Applications 7th Edition, Kenneth H. Rosen
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