What is Logic?
The foundation of reasoning, critical thinking, and formal analysis
Premises + Rules → Valid ConclusionsLogic is the systematic study of valid reasoning and inference. It provides the foundation for determining what conclusions validly follow from given premises.
Key Characteristics of Logic:
- • Systematic: Uses precise rules and methods
- • Universal: Applies across all domains of knowledge
- • Objective: Independent of personal beliefs or opinions
- • Formal: Uses symbols and structures to represent reasoning
Propositional Logic
Deals with propositions (statements that are true or false) and how they combine using logical connectives like "and," "or," and "if...then."
P ∧ Q → R✅ Current Focus: This is the main focus of this course and calculator!
Predicate Logic
Extends propositional logic to include quantifiers ("for all," "there exists") and predicates that describe properties of objects.
∀x (Human(x) → Mortal(x))🚧 Coming Soon: Predicate logic is not yet included in this course or calculator, but will be added in a future update!
Mathematics
- • Proofs and theorems
- • Set theory
- • Number theory
- • Abstract algebra
Computer Science
- • Programming logic
- • Database queries
- • Artificial intelligence
- • Circuit design
Philosophy
- • Argument analysis
- • Epistemology
- • Ethics reasoning
- • Metaphysics
Daily Life
- • Decision making
- • Problem solving
- • Evaluating news
- • Planning and organizing
Logical Reasoning in Action:
Premise 1: If it rains, then the ground gets wet.
Premise 2: It is raining.
Conclusion: Therefore, the ground gets wet.
This follows the logical pattern called Modus Ponens: If P implies Q, and P is true, then Q must be true.