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What does it mean if a line intersects a set?
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Illustrated definition of Intersect: To cross over (have some common point) The red and blue lines intersect.
Memorize the definitions of intersection, union, and set difference. We rely on them to prove or derive new results. The intersection of two sets A and B, denoted A ∩ B, is the set of elements common to both A and B. In symbols, ∀x ∈ U [x ∈ A ∩ B ⇔ (x ∈ A ∧ x ∈ B)].
Definition. The term “intersect” can be defined for both lines and sets. When we talk about an intersection in geometry, we mean that something cuts or passes through or across something. When we talk about the intersection of two sets, we mean the set of shared elements between them.
- Lines, Rays, Line Segments
- Other Geometric Figures
- Sets
For lines, rays, and line segments, intersect means to meet or cross. When two lines, rays, or line segments intersect, they have one common point.
Some geometric figures intersect at more than one point. When two distinct planesmeet, they intersect at a line. When a plane and a spheremeet, their intersection forms a circular section. In the diagram above, plane p intersects a sphere with center O forming a circle with center O. The circle is called a great circle of the sphere since it contai...
It is also possible for sets to intersect or share common elements. The Venn diagrambelow shows the intersection of multiples of 2 and multiples of 3 within the set of whole numbers from 1 to 12.
Example of Intersect. Any line segment that crosses or meets AD is said to intersect AD. In the given figure, the line segments AB, DC, DH, and AE intersect AD.
The intersection of two sets says A A and B B is the set that contains all the elements of set A A that also belong to set B B. It is denoted as: A A ∩ ∩ B B. The below-given image shows two sets, A A and B B, and their intersection.
In this example, the two given lines, Line 1 1 and Line 2 2, have one intersection point. The equation of Line 1 1 is y=x y = x and the equation of Line 2 is y=-\cfrac {1} {3} y = −31. The point of intersection (common point) is the ordered pair (0, 0). (0,0).
