# Common symbols used in set theory

S

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### Common symbols used in set theory

• 1. SET and Symbols 1 Common Symbols Used in Set Theory Symbols save time and space when writing. Here are the most common set symbols In the examples C = {1, 2, 3, 4} and D = {3, 4, 5} Symbol Meaning Example { } Set: a collection of elements {1, 2, 3, 4} A ∪ B Union: in A or B (or both) C ∪ D = {1, 2, 3, 4, 5} A ∩ B Intersection: in both A and B C ∩ D = {3, 4} A ⊆ B Subset: every element of A is in B. {3, 4, 5} ⊆ D A ⊂ B Proper Subset: every element of A is in B, but B has more elements. {3, 5} ⊂ D A ⊄ B Not a Subset: A is not a subset of B {1, 6} ⊄ C A ⊇ B Superset: A has same elements as B, or more {1, 2, 3} ⊇ {1, 2, 3} A ⊃ B Proper Superset: A has B's elements and more {1, 2, 3, 4} ⊃ {1, 2, 3} A ⊅ B Not a Superset: A is not a superset of B {1, 2, 6} ⊅ {1, 9} Ac Complement: elements not in A Dc = {1, 2, 6, 7} When set universal = {1, 2, 3, 4, 5, 6, 7} A − B Difference: in A but not in B {1, 2, 3, 4} − {3, 4} = {1, 2} a ∈ A Element of: a is in A 3 ∈ {1, 2, 3, 4} b ∉ A Not element of: b is not in A 6 ∉ {1, 2, 3, 4} ∅ Empty set = {} {1, 2} ∩ {3, 4} = Ø set universal Universal Set: set of all possible values (in the area of interest) P(A) Power Set: all subsets of A P({1, 2}) = { {}, {1}, {2}, {1, 2} } A = B Equality: both sets have the same members {3, 4, 5} = {5, 3, 4} A×B Cartesian Product (set of ordered pairs from A and B) {1, 2} × {3, 4}
• 2. SET and Symbols 2 = {(1, 3), (1, 4), (2, 3), (2, 4)} |A| Cardinality: the number of elements of set A |{3, 4}| = 2 | Such that { n | n > 0 } = {1, 2, 3,...} : Such that { n : n > 0 } = {1, 2, 3,...} ∀ For All ∀x>1, x2>x ∃ There Exists ∃ x | x2>x ∴ Therefore a=b ∴ b=a Natural Numbers Natural Numbers {1, 2, 3,...} or {0, 1, 2, 3,...} Integers Integers {..., −3, −2, −1, 0, 1, 2, 3, ...} Rational Numbers Rational Numbers Algebraic Numbers Algebraic Numbers Real Numbers Real Numbers Imaginary Numbers Imaginary Numbers 3i Complex Numbers Complex Numbers 2 + 5i
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