Notation

This is the notation resource.

Operator: Its simplest meaning in mathematics and logic, is an action or procedure which produces a new value from one or more input values. There a unary, binary, and ternary operators.

Arithmetic Operations...

Operator / Operation Notation Syntax Extra
Add, addition + A + B  
Subtract, subtraction - A - B  
Multiply, multiplication * or x A * B A + A + A...
Divide, division ÷ or / A ÷ B A ÷ A ÷ A...

Basic Relations...

Relation Notation Syntax Extra
Equals = A = B  
Not equals ≠or != or <> A≠B  
Greater than > A > B  
Less than < A < B  
Greater than or equals > or >= A > B  
Lesser than or equals < or <= A < B  

Set Theory Operations...

Operator / Operation Notation Syntax Extra
Union A ∪ B Or
Intersection A ∩ B And
Complement c Ac Set difference
Cartesian Product × A × B A set whose members are all possible ordered pairs (a,b)
Relative complement - or \ A - B All members from A that are not B. Belong to their union, but not intersection.
Symmetric difference ∆ or ⊖ A ∆ B Members belong to A or B, but not their intersection

Set Theory Relations...

Relation Notation Syntax English
Member / element of x ∈ A x "is a member of" set A
Not member / element of x ∉ A x "is not a member of" set A
Subset A ⊆ B set A "is a subset of" set B
Superset A ⊇ B set A "is a superset of" set B
Proper subset A ⊂ B Is a subset, and has less members than B
Proper superset A ⊃ B Is a superset, and has more members than B
Not subset A ⊄ B set A "is not a subset of" set B
Not superset A ⊅ B set A"is not a superset of" set B
Equality = A = B set A "has the same members as" set B

Set Theory Sets...

Set Notation Example Extra
Natural numbers N or ℕ1 1, 2, 3, 4, 5, 6, 7, 8 The counting numbers
Whole numbers W or ℕ0 0, 1, 2, 3, 4, 5, 6, 7, 8 Natural numbers, including zero
Integers Z or ℤ -4, -3, -2, -1, 0, 1, 2, 3, 4 Whole numbers, including negatives
Rational numbers Q or ℚ -4, -1.5, 1, 0, 2, 3.9, 6 Integers, including fractions
Real numbers R or ℝ -4, -1.5, 1, 0, 2, 3.9, 6, pi Rational numbers, including irrational numbers
Universal set U Anything Contains all sets
Empty / Null set Ø or 0 The set of squares with 5 sides A set with nothing inside of it

Boolean Logic...

      English Set Theory Set Theory
OR Logical disjunction A or B "or" A union B (exists in one of the sets) A ∪ B
AND Logical conjunction A and B "and" A intersect B (exists in both of the sets) A ∩ B
NOR Logical NOR Neither A or B "neither...nor" Not in A union B (exists in neither sets) Not ( A ∪ B )

Boolean Logic...

      English Set Theory Set Theory
XOR Exclusive disjunction A or B, not A and B   A union B, not A intersect B Symmetric difference
NAND Logical NAND Not A and B "not both" Not A intersect B NOT ( A ∩ B )
XNOR Logical biconditional A and B, or not A and B   A intersect B, or not A intersection B A ∩ B OR NOT ( A ∩ B )

Propositional Logic: Proposition Notations

Notation What It Is Example
P 1st proposition (left side) P ∧ Q, "P=black hair & Q=6 feet tall"
Q 2nd proposition (right side) P ∨ Q, "P=white skin & Q=blue eyes"

Predicate Logic: Quantifiers, Logical Connectives

Name Type Notation Informal  
Universal quantifier Quantifier "given any" or "for all" (x) is true for everything
Existential quantifier Quantifier "there exists" (x) is the predication of a property or relation to at least one member of the domain
Conjunction Logical connective ∧, &, · "and"  
Disjunction Logical connective "or"  
Implication Logical connective →, ⇒, ⊃ "implies", "if...then"  
Biconditional Logical connective ↔, ≡ , = "equals"  
Negation (not) Logical connective ¬, ~ "not"  
Contradiction Logical connective ⊥, 0, F    
Tautology Logical connective ⊤, 1, T    

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