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Propositional Logic Basics

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Questions and Answers

What is propositional logic the study of?

how simple statements are altered to form compound statements, and the way(s) in which truth is a function of the simple statements and the compounding elements.

What is a simple statement in propositional logic?

a statement that does not have any other statement as a component

What is the purpose of translating ordinary language statements into propositional logic notation?

to facilitate the study of propositional logic

What symbol is used to represent negation in propositional logic?

tilde Signup and view all the answers

What determines the truth value of a truth-functional compound proposition?

The truth values of its components and the definitions of the logical operators involved. Signup and view all the answers

What is the function of the dot symbol in propositional logic?

to represent conjunction, which conjoins two distinct statements Signup and view all the answers

What is a truth function?

A truth-functional compound proposition that can be determined by the truth values of its components and the definitions of the logical operators involved. Signup and view all the answers

What is a biconditional in propositional logic?

a compound statement made up of two conditionals Signup and view all the answers

What is a statement form?

A pattern of statement variables and logical operators. Signup and view all the answers

What is the goal when constructing compound statements in propositional logic?

to create well-formed formulas, which are grammatically correct compound statement forms Signup and view all the answers

What is the difference between inclusive and exclusive disjunction?

Inclusive disjunction allows both disjuncts to be true at the same time, while exclusive disjunction does not. Signup and view all the answers

What is a main operator in a compound statement?

the logical operator that has in its range the largest component or components in a compound statement Signup and view all the answers

What is the order of operations in a truth table?

A step-by-step method of generating a complete truth table, handling the logical operators in a specific order. Signup and view all the answers

What is a contingent statement?

A statement that is neither necessarily true nor necessarily false, but is sometimes true and sometimes false. Signup and view all the answers

What is a tautology?

A statement that is necessarily true. Signup and view all the answers

What does it mean for two statements to be logically equivalent?

Two truth-functional statements that appear different but have identical truth tables. Signup and view all the answers