MODULUS / REFERENCE
Formulas: Discrete mathematics
Complete Android Modulus reference: formulas for Discrete mathematics.
Logic and sets
• ¬A, A ∧ B, A ∨ B, A ⊕ B
• A → B ≡ ¬A ∨ B
• A ↔ B ≡ (A → B) ∧ (B → A)
• |A ∪ B| = |A| + |B| − |A ∩ B|
Relations and functions
• Reflexive: ∀x xRx
• Symmetric: xRy ⇒ yRx
• Transitive: xRy ∧ yRz ⇒ xRz
Graphs and trees
• Σ deg(v) = 2|E|
• For a tree: |E| = |V| − 1
• For a complete graph: |E| = n(n − 1) / 2
Recurrences and number theory
• an = c an−1 + d
• d = gcd(a, b), lcm(a, b) = |ab| / gcd(a, b)
• ab mod m — modular exponentiation
• ¬A, A ∧ B, A ∨ B, A ⊕ B
• A → B ≡ ¬A ∨ B
• A ↔ B ≡ (A → B) ∧ (B → A)
• |A ∪ B| = |A| + |B| − |A ∩ B|
Relations and functions
• Reflexive: ∀x xRx
• Symmetric: xRy ⇒ yRx
• Transitive: xRy ∧ yRz ⇒ xRz
Graphs and trees
• Σ deg(v) = 2|E|
• For a tree: |E| = |V| − 1
• For a complete graph: |E| = n(n − 1) / 2
Recurrences and number theory
• an = c an−1 + d
• d = gcd(a, b), lcm(a, b) = |ab| / gcd(a, b)
• ab mod m — modular exponentiation
Values are provided for reference. Check the required unit system and conditions before engineering or laboratory use.