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Intersections of the unaccented modern Greek, Latin, and Cyrillic scripts, considering only the shapes of the letters and ignoring their pronunciation Example of an intersection with sets The intersection of two sets A {\displaystyle A} and B , {\displaystyle B,} denoted by A ∩ B {\displaystyle A\cap B} , [ 3 ] is the set of all objects that ...
Intersection of the sets A and B, denoted A ∩ B, is the set of all objects that are members of both A and B. For example, the intersection of {1, 2, 3} and {2, 3, 4} is the set {2, 3}. Set difference of U and A, denoted U \ A, is the set of all members of U that are not members of A.
The intersection of A with any of B, C, D, or E is the empty set. In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at
The intersection is the meet/infimum of and with respect to because: if L ∩ R ⊆ L {\displaystyle L\cap R\subseteq L} and L ∩ R ⊆ R , {\displaystyle L\cap R\subseteq R,} and if Z {\displaystyle Z} is a set such that Z ⊆ L {\displaystyle Z\subseteq L} and Z ⊆ R {\displaystyle Z\subseteq R} then Z ⊆ L ∩ R . {\displaystyle Z ...
The intersection A ∩ B is the set of all things that are members of both A and B. Likewise, the intersection is formally defined by the corresponding logical conjunction (). Further, if there are no common elements between A and B, i.e. if the intersection of A and B is the empty set (A ∩ B = ∅), then A and B are said to be disjoint.
The combined region of the two sets is called their union, denoted by A ∪ B, where A is the orange circle and B the blue. The union in this case contains all living creatures that either are two-legged or can fly (or both). The region included in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A ∩ B.
The algebra of sets is the set-theoretic analogue of the algebra of numbers. Just as arithmetic addition and multiplication are associative and commutative, so are set union and intersection; just as the arithmetic relation "less than or equal" is reflexive, antisymmetric and transitive, so is the set relation of "subset".
Intersection distributes over union ... This idea subsumes the preceding sections—for example, A ∪ B ∪ C is the union of the collection {A, B, C}.