Connectives a summary of connectives Symbol Verbose name Remark V disjunction ∧ conjunction and negation not conditional if. then biconditional if and only if
Connectives A summary of connectives: Symbol Verbose name Remark ∨ disjunction or ∧ conjunction and ¬ negation not → conditional if ..., then ... ↔ biconditional if and only if Yi Li (Fudan University) Discrete Mathematics March 20, 2012 6 / 24
anguage o Symbols of propositional logic Connectives:V,∧,,→,分 e Parentheses O Propositional Letters: A, A1, A2, ...,B, B1, B2 o A propositional letter is the most elementary object
Language Symbols of propositional logic: 1 Connectives: ∨, ∧, ¬,→,↔ 2 Parentheses: ), ( 3 Propositional Letters: A, A1, A2, · · · , B, B1, B2, · · · . A propositional letter is the most elementary object. Yi Li (Fudan University) Discrete Mathematics March 20, 2012 7 / 24
Propositions Definition(Proposition) o Propositional letters are propositions o if a and B are propositions, then (aV3),(a^B),(-a),(a→B)and(a分)are propositions o A string of symbols is a proposition if and only if it can be obtained by starting with propositional letters(1)and repeatedly applying(2)
Propositions Definition (Proposition) 1 Propositional letters are propositions. 2 if α and β are propositions, then (α ∨ β),(α ∧ β),(¬α),(α → β) and (α ↔ β) are propositions. 3 A string of symbols is a proposition if and only if it can be obtained by starting with propositional letters (1) and repeatedly applying (2). Yi Li (Fudan University) Discrete Mathematics March 20, 2012 8 / 24