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Learn the definitions and properties of set operations such as intersection, union, difference, complement and symmetric difference. See examples, exercises and diagrams to illustrate the concepts.
- 4.4: Cartesian Products
Definition: Ordered Pair. An ordered pair \((x,y)\) consists...
- Subsets and Power Sets
Figure \(\PageIndex{1}\): The relationship among various...
- De Morgan's Laws
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- 4.4: Cartesian Products
Intersection (∩) is a symbol used in set theory to show the common elements between two sets. Learn how to use it, see examples, and find codes for inserting it in various formats.
Intersect. To cross over (have some common point) The red and blue lines intersect.
- Intersections and Subsets
- Commutative Law
- Associative Law
- Distributive Law
- De Morgan's Laws
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If set A is a subset of set B, then the intersection of the two sets is equal to set A. Using set notation: if A ⊆ B, then A ∩ B = A For example, if A = {4, 5, 6} and B = {4, 5, 6, 7, 8}, their intersection is {4, 5, 6}, or A.
The commutative law states that the order in which the intersection of two sets is taken does not matter. Given two sets, A and B: A ∩ B = B ∩ A Let A = {1, 2, 3} and B = {3, 5, 7}. The only common element the two sets have is 3. Thus, A ∩ B = B ∩ A = {3}. It doesn't matter whether we consider A or B first, the result will be the same.
The associative law states that rearranging the parentheses in an intersection of sets does not change the result. Given sets A, B, and C: (A ∩ B) ∩ C = A ∩ (B ∩ C) The position of the parentheses doesn't matter since the intersection operation does not change the relationship between the sets. Comparing sets A and B first, then B and C, or B and C...
For sets A, B, and C, the distributive law states A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) where A is distributed to B and C. This is similar to the distributive property of multiplication in which multiplication distributes over addition. The Venn diagram below demonstrates the first law listed above: From the figure, A = {1...
In set theory, De Morgan's laws are a set of rules that relate the union and intersection of sets through their complements.
Intersection is the set of elements that two or more sets have in common. Learn how to use Venn diagrams, symbols, and laws to find intersections of sets and their complements.
Intersect means to meet, cross, or overlap in geometry, and to share common elements in sets. Learn how to find the intersection of lines, rays, line segments, planes, spheres, and sets with diagrams and explanations.
Learn how to find the intersection of sets, which is the set of elements common to two or more sets. See the symbol, formula, Venn diagram and properties of intersection of sets with examples and practice problems.
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Learn what intersect means in geometry and set theory. See examples of intersecting lines, line segments, and sets, and how to find the point of intersection.
