Set Theory Symbols & Definitions

A^c or A'----- A raised to the power of c

Name: Complement Definition: All objects that do not belong to set A. Example: (none provided)

A = B

Name: Equality Definition: Set A & set B contain the same elements. Example: If set A = {2,3,4} & set B = {2,3,4} then A=B

A∩B

Name: Intersection Definition: Objects that belong to set A and set B Example:If set A = {1,2,3} & set B = {2,3,4} thenA∩B = {2,3}

A⊄B

Name: Not Subset Definition: Subset A does not have any matching elements of set B. Example: If set A = {a,b} & set B = {c,d,e,f} then A ⊄ B

A ⊅ B

Name: Not superset Definition: Set A is not a superset of set B if set A does not contains all of the elements of set B. Example: If set A = {a,f,c,d} & set B = {b,f} then A ⊅ B

Ø

Name: Null or empty set Definition: The set does not contain any elements. Example: if set A = { } then A =Ø

P(A) ---- http://prntscr.com/ejnupj

Name: Power set Definition: Power set is the set of all subsets of A, including the empty set and set A itself. Example: If set A = {1,2,3} then P(A) { }, {1}, {2}, {3}, {1,2), {1,3), {1,2,3)

A⊂B

Name: Proper subset (strict subset) Definition: Set A is a proper subset of set B if and only if every element in set A is also in set B, and there exists at least one element in set B that is not in set A. Example: {9,14} ⊂ {9,14,28}

A ⊃ B

Name: Proper superset Definition: Set A is a proper superset of set B if set A contains all of the elements of set B, and there exists at least one element in set A that is not in set B. Example: If set A = {4,5,6} & set B = {5,6} then A ⊃ B

A-B

Name: Relative complement Definition: Elements of set A but not set B Example: If set A = {a,b,c} & set B = {c,d,e} then A-B= {a,b}

{ }

Name: Set Definition: A collection of elements Example: A = {2,7,8,9,15,23,35}

(fancy C) ---- http://prntscr.com/ejnxtn

Name: Set of Complex Numbers Definition: (fancy C) = {z | z=a+bi, -∞<a<∞, -∞<b<∞} Example: 5 + 3i ∈ (fancy C)

(fancy Z) ---- http://prntscr.com/ejnxo1

Name: Set of Integer Numbers Definition: (fancy Z) = {... -4,-3,-2,-1,0,1,2,3,4, ...} Example: -2 ∈ (fancy Z)

(fancy N with subscript 0) ---- http://prntscr.com/ejnx04

Name: Set of Natural Numbers with Zero Definition: (fancy N subscript 0) = {0,1,2,3,4,5,6,7,8, ...} Example: 0∈ (fancy N subscript 0)

(fancy N with subscript 1) ---- http://prntscr.com/ejnxch

Name: Set of Natural Numbers without Zero Definition: (fancy N subscript 1) ={1,2,3,4,5,6,7,8, ...} Example: 7∈ (fancy N subscript 1)

(fancy Q) ---- http://prntscr.com/ejnxqf

Name: Set of Rational Numbers Definition:A rational number is a number that can be expressed as a fraction where p and q are integers and q does not equal zero. Example: 2/3 ∈ (fancy Q)

(fancy R) ---- http://prntscr.com/ejnxrm

Name: Set of Real Numbers Definition: (fancy R) = {x | -∞ < x <∞} Example: 4.862 ∈ (fancy R)

A⊆B

Name: Subset Definition: Set A is a subset of set B if and only if every element of set A is in set B. Example: {9,14,28} ⊆ {9,14,28}

A⊇B

Name: Superset Definition: Set A is a superset of set B if set A contains all of the elements of set B. Example: If set A = {d,e,f} & set B = {d,e,f} then A⊇B.

A∆B

Name: Symmetric Difference Definition: Elements that belong to set A or set B but not to their intersection. Example: If set A = {a,b,c} & set B = {c,d,e} then A∆B = {a,b,d,e}

A∪B

Name: Union Definition: objects that belong to set A or set B Example: A ∪ B = {3,7,9,14,28}

U

Name: Universal set Definition: The set of all possible elements Example: If set A = {1,2,3}, set B = {4,5,6} & set C = {7,8} then U = {1,2,3,4,5,6,7,8}

a∈A

Name: element of Definition: Membership of set A. Example:If set A = {a,b,e,f,g,h} then a∈A

x∉A

Name: not element of Definition: Not a member of set A. Example: x∉A