Connectives

used to generate new mathematical statements from combining one or more Propositions. These are called compound propositions or Compound_Propositions. Truth tables will be used to display the relationship between a formula and the propositions within it.

Notation

  • connectives : P,Q,R,etc

Types

Negation (¬)
not
Conjunction(∧)
and
Disjunction(∨)
or
Exclusive Or(⊕)
xor
Implication(➝)
implies
Logically equivalent
- base : p➝q
- contrapositive : ¬q➝¬p
--------------------
Logically equivalent
- converse : q➝p
- inverse : ¬p➝¬q
Biconditional( ⟷)
if and only if

Precedence

a propositions order of connectives matter.

  • order:
    • ∧
    • ∨
    • ➝
    • ⟷