Logic examines the structure of valid arguments. It asks: if the premises are true, does the conclusion necessarily follow? Formal logic uses symbols to represent statements and rules to derive conclusions. Aristotle's syllogisms were an early system; modern logic, developed by Frege, Russell, and others, underpins mathematics and computer science.

Propositional logic deals with statements that are true or false and connectives like AND, OR, and NOT. Predicate logic adds quantifiers: "for all" and "there exists." These systems formalize reasoning and reveal fallacies.

Logic is the foundation of mathematical proof. Every theorem rests on logical deduction from axioms. In computing, logic gates implement Boolean operations, and programming languages use logical conditions. The subject also intersects with philosophy, linguistics, and artificial intelligence. Clear thinking about reasoning is useful far beyond mathematics.

• Study of valid reasoning
• Uses symbols and formal rules
• Propositional and predicate logic
• Foundation of proof and computing