Nota tions
Sym bol
Mean ing
∅
Empty set
| S |
Car di nal ity of set S.
∪
Set Union
∩
Set Inter sec tion
a A
∈
a belongs to the set A
A B
⊆
A is a sub set of B
—
Set Dif fer ence
A
c
Com ple ment of A
2
A
Powerset of A
A B
×
Car te sian prod ucts of A and B
A i
i
n
=1
U
Union of sets A 1 , A 2 , ..... A n
L
Com ple ment of L
L
R
Lan guage Rever sal
L
*
Kleene Star
L
+
Kleene Plus
Σ
*
All finite strings over the alpha bet Σ
Σ
n
All strings over the alpha bet Σ of length exactly n.
λ
Empty string
| x |
Length of string x.
∨
The OR func tion
∧
The AND func tion
x y
ℜ
x is related to y under rela tion ℜ
R
+
Tran si tive clo sure of R
R R
1
2
o
Com pos ite of rela tions R 1 and R 2
f x
y
: →
Func tion from x to y.
f x
( )
Image of x under f.
Sym bol
Mean ing
∅
Empty set
| S |
Car di nal ity of set S.
∪
Set Union
∩
Set Inter sec tion
a A
∈
a belongs to the set A
A B
⊆
A is a sub set of B
—
Set Dif fer ence
A
c
Com ple ment of A
2
A
Powerset of A
A B
×
Car te sian prod ucts of A and B
A i
i
n
=1
U
Union of sets A 1 , A 2 , ..... A n
L
Com ple ment of L
L
R
Lan guage Rever sal
L
*
Kleene Star
L
+
Kleene Plus
Σ
*
All finite strings over the alpha bet Σ
Σ
n
All strings over the alpha bet Σ of length exactly n.
λ
Empty string
| x |
Length of string x.
∨
The OR func tion
∧
The AND func tion
x y
ℜ
x is related to y under rela tion ℜ
R
+
Tran si tive clo sure of R
R R
1
2
o
Com pos ite of rela tions R 1 and R 2
f x
y
: →
Func tion from x to y.
f x
( )
Image of x under f.