logic
Logic & Propositions
Master the foundations of mathematical reasoning: propositions, logical connectives, truth tables, and equivalences.
4 subtopics8 formulas77 problemsin progress
Discrete math, taught interactively
Discretica
Interactive discrete math for CS students: topics, proof trainer, practice, and browser-native tools.
7topics
534problems
54formulas
60proof tasks
Topics
Study library
Search and drill into the same localized lessons, formulas, and problem coverage from the mobile app.
logic-propositions
Propositions & Truth Values
Learn what propositions are and how truth values work
8 lessons
logic-connectives
Logical Connectives
Understand AND, OR, NOT, implication, and biconditional
8 lessonspremium
logic-truth-tables
Truth Tables
Construct and analyze truth tables for compound propositions
7 lessonspremium
logic-equivalences
Logical Equivalences
Master key equivalence laws used to simplify logical expressions
8 lessonspremium
Formula sheet
8 formulas
De Morgan's Law (AND)
¬(p ∧ q) ≡ ¬p ∨ ¬qThe negation of a conjunction is the disjunction of the negationsDe Morgan's Law (OR)
¬(p ∨ q) ≡ ¬p ∧ ¬qThe negation of a disjunction is the conjunction of the negationsConditional Equivalence
p → q ≡ ¬p ∨ qAn implication is equivalent to the disjunction of the negated hypothesis and the conclusionContrapositive
p → q ≡ ¬q → ¬pAn implication is logically equivalent to its contrapositiveBiconditional Expansion
p ↔ q ≡ (p → q) ∧ (q → p)A biconditional is the conjunction of both directions of implicationDistributive Law (AND over OR)
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)Conjunction distributes over disjunctionDistributive Law (OR over AND)
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)Disjunction distributes over conjunctionAbsorption Law (1)
p ∨ (p ∧ q) ≡ pA variable absorbs its conjunction with anotherPrivate notes