Math Symbols
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In the examples C = {1,2,3,4} and D = {3,4,5}
SymbolMeaningExample{ }Set: a collection of elements{1,2,3,4}A ∪ BUnion: in A or B (or both)C ∪ D = {1,2,3,4,5}A ∩ BIntersection: in both A and BC ∩ D = {3,4}A ⊆ BSubset: A has some (or all) elements of B{3,4,5} ⊆ DA ⊂ BProper Subset: A has some elements of B{3,5} ⊂ DA ⊄ BNot a Subset: A is not a subset of B{1,6} ⊄ CA ⊇ BSuperset: A has same elements as B, or more{1,2,3} ⊇ {1,2,3}A ⊃ BProper Superset: A has B's elements and more{1,2,3,4} ⊃ {1,2,3}A ⊅ BNot a Superset: A is not a superset of B{1,2,6} ⊅ {1,9}AcComplement: elements not in ADc = {1,2,6,7}
When
= {1,2,3,4,5,6,7}A − BDifference: in A but not in B{1,2,3,4} − {3,4} = {1,2}a ∈ AElement of: a is in A3 ∈ {1,2,3,4}b ∉ ANot element of: b is not in A6 ∉ {1,2,3,4}∅Empty set = {}{1,2} ∩ {3,4} = ØUniversal Set: set of all possible values
(in the area of interest) P(A)Power Set: all subsets of AP({1,2}) = { {}, {1}, {2}, {1,2} }A = BEquality: both sets have the same members{3,4,5} = {5,3,4}A×BCartesian Product
(set of ordered pairs from A and B){1,2} × {3,4}
= {(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,...}
When
= {1,2,3,4,5,6,7}A − BDifference: in A but not in B{1,2,3,4} − {3,4} = {1,2}a ∈ AElement of: a is in A3 ∈ {1,2,3,4}b ∉ ANot element of: b is not in A6 ∉ {1,2,3,4}∅Empty set = {}{1,2} ∩ {3,4} = ØUniversal Set: set of all possible values(in the area of interest) P(A)Power Set: all subsets of AP({1,2}) = { {}, {1}, {2}, {1,2} }A = BEquality: both sets have the same members{3,4,5} = {5,3,4}A×BCartesian Product
(set of ordered pairs from A and B){1,2} × {3,4}
= {(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,...}