Logic
Logic is the branch of mathematics that studies the rules of reasoning. WIIS provides structured learning materials focusing on propositional logic and predicate logic, including logical operations, logical equivalences, quantifiers, and rules of inference. By understanding the logical structure that underlies mathematical proof, learners develop the ability to read and construct definitions, theorems, and proofs, while building a foundation for set theory, real analysis, and university-level mathematics as a whole.
Fields of Logic
Propositional logic is a foundational area of logic for studying the rules of mathematical reasoning. Learn logical operations, truth tables, logical equivalences, and rules of inference systematically, and build a foundation for university-level mathematics, including set theory and analysis.
Whereas the basic units of propositional logic are propositional variables, the basic units of predicate logic are concepts called propositional functions. This makes it possible to express a broader range of statements and also introduces operations known as quantification.
New Materials
Double negation introduction also holds in predicate logic. That is, from any formula \(A\), we may derive its double negation \(\lnot\lnot A\).
Double negation elimination also holds in predicate logic. That is, for any formula \(A\), we may derive \(A\) from the double negation \(\lnot\lnot A\).
Disjunction introduction also holds in predicate logic. That is, for formulas \(A\) and \(B\), from \(A\) we may derive the disjunction \(A\vee B\), and from \(B\) we may likewise derive the disjunction \(A\vee B\).
Disjunction elimination also holds in predicate logic. That is, for formulas \(A\), \(B\), and \(C\), from \(A\rightarrow C\), \(B\rightarrow C\), and \(A\vee B\), we may derive \(C\).
Conjunction introduction also holds in predicate logic. That is, from formulas \(A\) and \(B\), we may derive the conjunction \(A\wedge B\).
Conjunction elimination also holds in predicate logic. That is, from the conjunction \(A\wedge B\), we may derive either \(A\) or \(B\).
Learning Guide
Related Fields
Set theory is the common language of modern mathematics. Focusing on sets, functions, relations, cardinality, and order relations, this course systematically explains the fundamental concepts needed to understand a wide range of mathematical fields. It provides a foundation for further study in areas such as real analysis, linear algebra, and topology.
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