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Set - Intersections | | Set - Intersections: Encyclopedia II - Set - Intersections | | A new set can also be constructed by determining which members two sets have "in common". The intersection of A and B, denoted by A ∩ B, is the set of all things which are members of both A and B. If A ∩ B = ø, then A and B are said to be disjoint.
Examples:
{1, 2} ∩ {red, white} = ø
{1, 2, green} ∩ {red, white, green} = {green}
{1, 2} ∩ ...
See also:Set, Set - Definition, Set - Describing sets, Set - Descriptions using words or lists, Set - Descriptions using mathematical notation, Set - Set membership, Set - Cardinality of a set, Set - Subsets, Set - Special sets, Set - Unions, Set - Intersections, Set - Complements | | | Set, Set - Cardinality of a set, Set - Complements, Set - Definition, Set - Describing sets, Set - Descriptions using mathematical notation, Set - Descriptions using words or lists, Set - Intersections, Set - Set membership, Set - Special sets, Set - Subsets, Set - Unions, Alternative set theory, Class (set theory), Family (mathematics), Mathematical structure, Multiset, Tuple | | |
| | | Set: Encyclopedia II - Set - Intersections
Set - Intersections
A new set can also be constructed by determining which members two sets have "in common". The intersection of A and B, denoted by A ∩ B, is the set of all things which are members of both A and B. If A ∩ B = ø, then A and B are said to be disjoint.
Examples:
- {1, 2} ∩ {red, white} = ø
- {1, 2, green} ∩ {red, white, green} = {green}
- {1, 2} ∩ {1, 2} = {1, 2}
Some basic properties of intersections:
- A ∩ B = B ∩ A
- A ∩ B is a subset of A
- A ∩ A = A
- A ∩ ø = ø
For more information about intersections of sets, see Intersection (set theory).
Other related archives19th century, Alternative set theory, Class (set theory), Complement (set theory), Empty set, Family (mathematics), French flag, Intersection (set theory), Mathematical structure, Multiset, Set theory, Set-builder notation, Subset, Tuple, Union (set theory), axiomatic, axiomatic set theory, braces, cardinal number, cardinality, collection, combinatorics, complex numbers, concepts, elements, ellipsis, equality, expression, improper fractions, infinity, integers, intuitive, irrational, mathematics, mathematics education, multiset, naive set theory, natural numbers, permutations and combinations, powers of two, primary school, proper, rational numbers, real numbers, relationship, set theory, theory, universal set, whole, whole numbers
 Adapted from the Wikipedia article "Intersections", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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