logic

overview

logical reasoning and mathematical thinking form the foundation of problem-solving in programming and engineering.

formal logic basics

propositional logic

• statements that are either true or false
• logical operators: and (∧), or (∨), not (¬), implies (→)
• truth tables for evaluating complex expressions
• useful for boolean algebra and digital circuit design

predicate logic

• statements with variables and quantifiers
• universal quantifier (∀) - "for all"
• existential quantifier (∃) - "there exists"
• more expressive than propositional logic

practical applications

programming logic

• conditional statements (if-then-else)
• boolean expressions and short-circuit evaluation
• loop invariants and termination conditions
• debugging by tracing logical flow

digital electronics

• boolean algebra for circuit design
• logic gates (and, or, not, xor)
• karnaugh maps for simplifying expressions
• building complex circuits from basic gates

mathematical reasoning

• proof techniques: direct, contradiction, induction
• logical equivalences and transformations
• set theory and logical operations
• understanding mathematical statements and proofs

thinking tools

problem decomposition

• breaking complex problems into logical steps
• identifying assumptions and constraints
• distinguishing between necessary and sufficient conditions
• recognizing patterns and logical structures

debugging methodology

• systematic elimination of possibilities
• hypothesis testing and validation
• understanding cause-and-effect relationships
• tracing logical flow to find errors

common logical fallacies

• correlation vs causation
• hasty generalization
• false dichotomy
• circular reasoning
• ad hominem attacks

avoiding these improves both technical and everyday reasoning.

related topics

• Semiconductors - for boolean algebra in electronics
• Philosophy - for systematic thinking approaches
• C Programming - for logical program structure