====== SET THEORY SYMBOLS ======


^ Hindi  ^  Symbol          ^  Symbol Name                                          ^  Meaning / definition                                         ^  Example                                        ^
|        |  { }             |  set                                                  |  a collection of elements                                     |  A = {3,7,9,14}, B = {9,14,28}                  |
|        |  A ∩ B           |  intersection                                         |  objects that belong to set A and set B                       |  A ∩ B = {9,14}                                 |
|        |  A ∪ B           |  union                                                |  objects that belong to set A or set B                        |  A ∪ B = {3,7,9,14,28}                          |
|        |  A ⊆ B           |  subset                                               |  A is a subset of B. set A is included in set B.              |  {9,14,28} ⊆ {9,14,28}                          |
|        |  A ⊂ B           |  proper subset / strict subset                        |  A is a subset of B, but A is not equal to B.                 |  {9,14} ⊂ {9,14,28}                             |
|        |  A ⊄ B           |  not subset                                           |  set A is not a subset of set B                               |  {9,66} ⊄ {9,14,28}                             |
|        |  A ⊇ B           |  superset                                             |  A is a superset of B. set A includes set B                   |  {9,14,28} ⊇ {9,14,28}                          |
|        |  A ⊃ B           |  proper superset / strict superset                    |  A is a superset of B, but B is not equal to A.               |  {9,14,28} ⊃ {9,14}                             |
|        |  A ⊅ B           |  not superset                                         |  set A is not a superset of set B                             |  {9,14,28} ⊅ {9,66}                             |
|        |  2A              |  power set                                            |  all subsets of A                                             |                                                 |
|        |  \mathcal{P}(A)  |  power set                                            |  all subsets of A                                             |                                                 |
|        |  A = B           |  equality                                             |  both sets have the same members                              |  A={3,9,14}, B={3,9,14}, A=B                    |
|        |  Ac              |  complement                                           |  all the objects that do not belong to set A                  |                                                 |
|        |  A \ B           |  relative complement                                  |  objects that belong to A and not to B                        |  A = {3,9,14}, B = {1,2,3},A-B = {9,14}         |
|        |  A - B           |  relative complement                                  |  objects that belong to A and not to B                        |  A = {3,9,14}, B = {1,2,3}, A-B = {9,14}        |
|        |  A ∆ B           |  symmetric difference                                 |  objects that belong to A or B but not to their intersection  |  A = {3,9,14}, B = {1,2,3}, A ∆ B = {1,2,9,14}  |
|        |  A ⊖ B           |  symmetric difference                                 |  objects that belong to A or B but not to their intersection  |  A = {3,9,14}, B = {1,2,3}, A ⊖ B = {1,2,9,14}  |
|        |  a∈A             |  element of , belongs to                              |  set membership                                               |  A={3,9,14}, 3 ∈ A                              |
|        |                  |                                                       |                                                               |                                                 |
|        |  x∉A             |  not element of                                       |  no set membership                                            |  A={3,9,14}, 1 ∉ A                              |
|        |  (a,b)           |  ordered pair                                         |  collection of 2 elements                                     |                                                 |
|        |  A×B             | cartesian product                                     |  set of all ordered pairs from A and B                        |  A×B = {(a,b)｜a∈A , b∈B}                       |
|        |  ｜A｜           |  cardinality                                          |  the number of elements of set A                              |  A={3,9,14}, ｜A｜=3                            |
|        |  #A              |  cardinality                                          |  the number of elements of set A                              |  A={3,9,14}, #A=3                               |
|        |  ｜              |  vertical bar                                         |  such that                                                    |  A={x｜3<x<14}                                  |
|        |                  |  aleph-null                                           |  infinite cardinality of natural numbers set                  |                                                 |
|        |                  |  aleph-one                                            |  cardinality of countable ordinal numbers set                 |                                                 |
|        |  Ø               |  empty set                                            |  Ø = { }                                                      |  C = {Ø}                                        |
|        |  U}              |  universal set                                        |  set of all possible values                                   |                                                 |
|        |  {N}0            |  natural numbers / whole numbers  set (with zero)     |  \mathbb{N}0 = {0,1,2,3,4,...}                                |  0 ∈ \mathbb{N}0                                |
|        |  {N}1            |  natural numbers / whole numbers  set (without zero)  |  \mathbb{N}1 = {1,2,3,4,5,...}                                |  6 ∈ \mathbb{N}1                                |
|        |  {Z}             |  integer numbers set                                  |  \mathbb{Z} = {...-3,-2,-1,0,1,2,3,...}                       |  -6 ∈ \mathbb{Z}                                |
|        |  {Q}             |  rational numbers set                                 |  \mathbb{Q} = {x ｜ x=a/b, a,b∈\mathbb{Z}}                    |  2/6 ∈ \mathbb{Q}                               |
|        |  {R}             |  real numbers set                                     |  \mathbb{R} = {x ｜ -∞ < x <∞}                                |  6.343434∈\mathbb{R}                            |
|        |  {C}             |  complex numbers set                                  |  \mathbb{C} = {z ｜ z=a+bi, -∞<a<∞,      -∞<b<∞}              |  6+2i ∈ \mathbb{C}                              |