List of Important Symbols
Symbol 
Meaning 
Section in which the symbol and its explanation appear first 

a ∈ A 
a belongs to the set A 
1.1 
a ∉ A 
a does not belong to the set A 
1.1 
Ø 
Empty set (Phi) 
1.1.2 
⇔ 
If and only if 
1.1.3 
A 
Cardinality of A 
1.1.3 
A ⊆ B 
A is a subset of the set B 
1.1.4 
A ⊂ B 
A is proper subset of the set B 
1.1.4 
℘(A) 
Power set of A 
1.1.5 
A ∪ B 
Union of sets A and B 
1.1.6 
A ∩ B 
Intersection of sets A and B 
1.1.6 
A − B 
Complement of B in A 
1.1.6 
A′ 
Complement of A 
1.1.6 
<a, b> 
Ordered pair 
1.1.10 
A × B 
Cartesian product 
1.1.11 
aRb or Rab 
a is related to b under the relation R 
1.2 
R′ 
Complement of relation 
1.2.3 
R^{−1} 
Inverse of relation R 
1.2.3 
F(x) 
Image of x under f 
1.3 
F: A → B 
Function from A to B 
1.3.2 
G Ο F 
Composition of F and G 
1.3.2 
idA or IA 
identity function on A 
1.3.2 
∑ 
Alphabet set 
1.4 
∑* 
Set of all strings over alphabet ∑ 
1.4 
∑+ 
Set of all strings over nonempty alphabet ∑ 
1.4 
ε 
Empty string or epsilon 
1.4 
A grammar 
1.4.2 

α 
String of terminals and nonterminals 
1.4.3 
B 
String of terminals and nonterminals 
1.4.3 
Δ 
Transition function 
2.1 
Q 
Set of states 
2.1 
F 
Set of final states 
2.1 
∈ 
Belongs to 
2.4 
Extended transition function 
2.6.1 

∪εclosure 
Union of null closure of 
2.6.1 
∏_{k} 
kEquivalence class 
2.8.3 
⇒ 
Implies 
2.8.2 
Δ 
Set of output symbols 
2.9.1 
Λ 
Out function 
2.9.1 
R 
Regular expression 
3.3 
h 
Homomorphism function 
3.9 
A α 
A derives α on one or more substitutions 
4.10 
A ⇒ α 
A derives α on single substitutions 
4.10 
Γ 
Stack symbols 
5.1.1 
Z_{0} 
Initial stack symbol 
5.1.1 
γ 
The content of the stack read from top to bottom 
5.1.3 
(q, x, s) (q, ε, α) 
Left configuration derives the right configuration on machine M on one or more derivations 
5.4.1 
B 
Blank symbol on tape 
6.1.1 
<l, q, r> 
Instantaneous description of TM 
6.1.2 
√ 
Check of symbol 
6.3.3 
# 
Special tape symbol 
6.5 
Ø, $ 
Special tapeend markers in LBA 
6.10 
∀ 
For all values of 

Summation series for values of j varying from 1 to n 

˥ 
Negation or NOT 
11.2 
∧ 
Conjunction or AND 
11.2 
∨ 
Disjunction or OR 
11.2 
→ 
Implication or IF..THEN.. 
11.2 
↔ 
Biconditional 
11.2 
Ǝ 
There exists 
11.8 