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Discrete mathematics - Coggle Diagram
Discrete mathematics
Sets and Logic
Propositions
= declarative statements about something true or false (NOT BOTH)
Atomic
The propositions will be known as the atomic propositions if
it will not further divided
.
It is used to have a single proposition symbol. Atomic propositions are indicated by small letters such as p, q, r, s, etc
Compound
Logical connectivity
operators used to connect one or more than one propositions or predicate logic
Types
Negation
Conjunction
When p and q are true, then the conjunction of them will be true.
When p and q are false, then the conjunction of them will be false.
Disjunction
When p and q are false, then the disjunction of them will be false.
When either p or q or both are true, then the disjunction of them will be true.
Conditional
The only false condition => p = True, q = False
Bi-conditional
When both p and q are true, or p and q both are false, then the bi-implication of them will be true.
In all the other cases, then the bi-conditional of them will be false.
Key properties
Double Negation: ¬(¬p) ≡ p
De Morgan's Law
¬(p ∧ q) ≡ ¬p ∨ ¬q
¬(p ∨ q) ≡ ¬p ∧ ¬q
Implication: p → q ≡ ¬p ∨ q
Contradiction: p ∧ ¬p ≡ F (always false)
Tautology: p ∨ ¬p ≡ T (always true)
The commutative and associative properties are contained by the negation, disjunction, conjunction, and bi-implication or bi-conditional.
Commutative or associative properties do not contain by implication or conditional.
Non-propositions
Combinatorics
