GE 04 - Elementary Logic, Reasoning, and Problem Solving

Vocabulary flashcards covering elementary logic, propositional connectives, truth tables, types of reasoning, and Polya's problem-solving framework from GE 04.

Logic

The science or study of how to evaluate arguments and reasoning, dealing with the methods of reasoning and how we think.

Propositional Logic

A branch of logic involving statements (propositions) that can be either true or false and uses logical connectives to form compound statements.

Logical Connectives

Operators defined by truth tables that have English language counterparts used to join or modify propositions.

Conjunction

A logical connective represented mathematically by $\wedge$ and in English as "And", where the statement $P \wedge Q$ is true only when both propositions $P$ and $Q$ are true.

Disjunction

A logical connective represented mathematically by $\vee$ and in English as "Or (inclusive)", where the statement $P \vee Q$ is true if at least one of $P$ or $Q$ is true.

Negation

A logical connective represented mathematically by $\sim$ or $\neg$ and in English as "Not", which reverses the truth value of a statement.

Conditional

A logical connective represented mathematically by $\rightarrow$ and in English as "If … then", where the statement $P \rightarrow Q$ is only false if $P$ is true and $Q$ is false.

Biconditional

A logical connective represented mathematically by $\leftrightarrow$ and in English as "If and only if", where the statement $P \leftrightarrow Q$ is true when both statements are either true or false.

Truth Table

A mathematical table used to display the truth values of logical expressions based on the truth values of their component propositions.

Inductive Reasoning

The process of drawing a general conclusion based on specific observations or examples, starting with specific cases and ending with a general conclusion.

Deductive Reasoning

The process of applying a general rule or principle to reach a specific conclusion, starting with a general statement and ending with a specific conclusion.

Polya's Four Steps in Problem Solving

A four-step framework used in mathematics and real life: 1. Understand the problem, 2. Devise a plan, 3. Carry out the plan, and 4. Look back and reflect.