RMU – Computer and Information Systems

INFS3450 - §1.3

Symbols, Signs, Operators

 Symbol BA = Boolean Algebra negation not Ø ~ BA: ′ conjunction and Ù & BA: • disjunction or Ú BA: + exclusive or xor Å BA: Å nand nand h nor nor ¯ conditional, material implication, implies If… then… ® ÉÞ biconditional, material equivalence …if and only if… ≡ «Û identity = non-identity ¹ universal quantifier for all " existential quantifier for some, for at least one… \$ subset; A is a subset of B: A Í B; B Ê A Í  Ê proper subset A is a proper subset of B Ì  É membership is a member of Î non-membership is not a member of Ï union member of either set or both È intersection member of both sets Ç Cartesian product or Cross-Join (ordered pairs, tuples) ´ (cross-join) Join Symbols Join, Equijoin, Natural Join, Inner Join Theta Join Semi-join Outer Join (Left, Right, Full) Anti-join Join (on =) Join (on θ) Where = Where θ Join (+) ⨝ (join) ⋉ (semi-join) ⟕ (left outer join) ⟖ (right outer join) ⟗ (full outer join) ⨞ (anti-join) set difference, minus, except A-B or A/B (members of A except those also in B) member of 1st set but not the 2nd - or / symmetric set difference (A Å B) ≡ (A - B) È (B - A) Å Δ Set (delimiters) set: {  } Sequence (delimiters) sequence: ⟨ ⟩ String (delimiters) string: "  " Multiset/Bag (delimiters) multiset/bag: ⟦  ⟧ the set of integers double-struck Z Z ℤ the set of non-negative integers; natural numbers; ℕ ⊂ ℤ double-struck N N ℕ the set of positive integers Z+ the set of real numbers;  ℕ ⊂ ℤ ⊂ ℝ double-struck R ℝ set replacement fat dot · power set; the set of all subsets (of A) double-struck P P ℙ maplet maps to ↦ cardinality (of a set X) |X| or #X complement (of A), non-A _ A relation ⟷ domain (of function or relation) domain of dom range (of function or relation) range of ran injection dom = S; ran Ì T ⤔ or ↣ surjection dom = S; ran = T ⤀ or ↠ bijection dom = S; ran = T ⤚↠ partial function dom Ì S ⇸ total function dom = S → relational composition ⨾ relational inverse of R R~

Fonts to use for less common symbols (Windows 7): Symbol, Cambria Math, Zed(Z)

References

[DEA1997] Neville Dean, The Essence of Discrete Mathematics (Pearson Prentice Hall, 1997).

[BAR1993:4] Jon Barwise and John Etchmendy, Tarski’s World (CLSI, 1993)

Updated: 2011-02-13