daee7902-f176-460d-997c-1366fbd324b1 81 4 5 false false 0 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]
 <p>Sets</p>

Binary set operations

X O Y S R Ø : Q R : k 0 : n 0 : 1 4 mat O ∈ ≡ R X Ø ≡ ( Y transpose X 1 findrows 0 ≠ ( | : O \00AC\ ≡ y Y y ∈ X S Ø ≡ R 1 k k 1 + : el y : continue if for O ⊆ ≡ R X ∩ Y S X ≡ ( : O ∪ ≡ x X R 1 k k 1 + : el x : for y Y R 1 k k 1 + : el y : for R R S : 3 1 line O ∩ ≡ x X y Y x y ≡ R 1 k k 1 + : el x : continue if for for O × ≡ x X y Y R 1 k k 1 + : el x y 1 2 mat : for for Bad Operator error if if if if if if R 3 1 line :

Set constructor

X S R Ø : Q R : n 0 : 1 3 mat x X x 0 ≡ ( Û transpose x 1 findrows 0 ≡ ( | 0 Q n n 1 + : el x : if for n 2 < R Q : Q Q 1 csort : R 1 el Q 1 el : k 1 : 1 3 mat ν 2 n range Q ν el Q ν 1 - el ≡ continue R 1 k k 1 + : el Q ν el : if for 2 1 line if R 4 1 line :

Unary set operations

O X S O \00AC\ ≡ X Ø ≡ Û X Û ≡ Ø X \00AC\ Û S if if Bad Operator error if 1 1 line :

Empty set

Ø 0 :

It could be also

ToDo: ⊂

 <p>Sets demo</p>

Universal Set

User defined universe.

Set Definitions

 2 3 4 7 9 1 5 mat 2 3 8 1 3 mat 2 4 1 2 mat

Empty set

 0 0 2 1 1 mat 0

Unary operations

 1 5 6 8 10 1 5 mat 1

Complement

 1

Binary operations

 2 3 1 2 mat 2 3 4 7 8 9 1 6 mat 0 2 3 4 7 9 1 5 mat 3 1 1 mat 3 1 1 mat 0 2 3 1 2 mat 1 1

Bilateral Neutrals

 1 1 8 1 1 mat 4 7 9 1 3 mat

Binary questions

 1 1 0 0 1 1

Fundamental laws of set algebra

Commutative laws:

 1 1

Associative laws:

 1 1

Distributive laws:

 1 1

Cartesian Product

 2 2 1 2 mat 2 3 1 2 mat 2 8 1 2 mat 3 2 1 2 mat 3 3 1 2 mat 3 8 1 2 mat 4 2 1 2 mat 4 3 1 2 mat 4 8 1 2 mat 1 9 mat

Notice that

 0

is empty in the given universe 'Û

Set operations could be used as indeces for an image universal set:

 b c d g i 5 1 mat b c h 3 1 mat b c d g h i 6 1 mat b c 2 1 mat

For get the results as row vectors use

 b c d g i 1 5 mat