7.1: Symbolizing English Arguments To symbolize statements properly, we must distinguish atomic from compound statements o Atomic Statements : those that do not have any other statement as a component We assign each atomic statement its own distinct capital letter This helps us provide a scheme of abbreviation o Compound Statements : those that have at least one atomic statement as a component We will symbolize English expressions by means of logical operators Operator Name Translates Type of Compound ~ Tilde Not Negation Dot And Conjunction Vee Or Disjunction Arrow If-then Conditional Double-arrow If and only if Biconditional Main logical operator : in a compound statement it is the one that governs the largest component or components of a compound statement Minor logical operator : part of the compound statement that governs smaller components Negations: o The tilde (~) is used to symbolize the word "not" and its stylistic variants o Negations are the opposite of the original statement o Roses are not blue. R: Roses are blue. ~R: Roses are not blue Conjunctions: o The dot ( ) translates the word "and" and all its stylistic variants o The statements that compose conjunctions are called conjuncts A conjunction is only true when both its conjuncts are true o Conjuncts are normally used to a relationship Disjunctions: o The vee ( ) symbolizes disjunctions with the word "or" and all its stylistic variants o
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- Fall '08
- Logic, Logical connective, truth values, atomic components