Connectives, also known as logical operators, are symbols used in formal [[Logic]] to combine simple statements into more complex ones. They are fundamental to both [[Truth-Functional Logic]] (TFL) and [[First-Order Logic]] (FOL). ## Main Types of Connectives 1. [[Negation]] (¬): "not" - Flips the truth value of a statement - Example: ¬P means "It is not the case that P" 2. [[Conjunction]] (∧): "and" - True only when both conjuncts are true - Example: P ∧ Q means "P and Q" 3. [[Disjunction]] (∨): "or" - True when at least one disjunct is true - Example: P ∨ Q means "P or Q" (inclusive or) 4. [[Conditional]] (→): "if...then" - False only when the antecedent is true and the consequent false - Example: P → Q means "If P, then Q" 5. [[Biconditional]] (↔): "if and only if" - True when both components have the same truth value - Example: P ↔ Q means "P if and only if Q" ## Properties - Truth-Functionality: The truth value of a complex statement formed with connectives depends only on the truth values of its components. - Scope: Connectives can be nested, with parentheses used to indicate the scope of each operator. ## Importance in Logic Connectives are essential for: 1. Building complex statements from simple ones 2. Analyzing the logical structure of arguments 3. Constructing [[Truth Tables]] 4. Formulating rules in [[Natural Deduction]] Understanding connectives and their properties is crucial for mastering formal [[Logic]] and developing skills in logical reasoning and analysis.