RMU Computer and Information Systems

INFS3450 - 1.3

Symbols, Signs, Operators

 

 

Symbol
BA = Boolean Algebra

negation

not

~
BA: ′

conjunction

and

&
BA:

disjunction

or


BA: +

exclusive or

xor

BA:

nand

nand

h

nor

nor

conditional, material implication, implies

If then

biconditional, material equivalence

if and only if

identity

 

=

non-identity

 

universal quantifier

for all

"

existential quantifier

for some, for at least one

$

subset;
A is a subset of B:
A
B; B A

 

proper subset

A is a proper subset of B

 

membership

is a member of

non-membership

is not a member of

union

member of either set or both

intersection

member of both sets

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 B) ≡
(A
- B)
(B
- A)

Δ

Set (delimiters)

set:

{ }

Sequence (delimiters)

sequence:

String (delimiters)

string:

" "

Multiset/Bag (delimiters)

multiset/bag:

the set of integers

double-struck Z

Z

the set of non-negative integers; natural numbers; ℕ ⊂ ℤ

double-struck N

N

the set of positive integers

 

Z+

the set of real numbers;
ℕ ⊂ ℤ ⊂

double-struck R

set replacement

fat dot

power set; the set of all subsets (of A)

double-struck 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 T

⤔ or ↣

surjection

dom = S; ran = T

⤀ or ↠

bijection

dom = S; ran = T

⤚↠

partial function

dom 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, Tarskis World (CLSI, 1993)

Updated: 2011-02-13