A subset B then A intersection set B =A example
Answers
Step-by-step explanation:
The intersection of two sets A and B, denoted by A ∩ B, is the set of all objects that are members of both the sets A and B. In symbols,
{\displaystyle A\cap B=\{x:x\in A{\text{ and }}x\in B\}.}
That is, x is an element of the intersection A ∩ B if and only if x is both an element of A and an element of B.
For example:
The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}.
The number 9 is not in the intersection of the set of prime numbers {2, 3, 5, 7, 11, ...} and the set of odd numbers {1, 3, 5, 7, 9, 11, ...}, because 9 is not prime.
Intersection is an associative operation; that is, for any sets A, B, and C, one has A ∩ (B ∩ C) = (A ∩ B) ∩ C. Intersection is also commutative; for any A and B, one has A ∩ B = B ∩ A. It thus makes sense to talk about intersections of multiple sets. The intersection of A, B, C, and D, for example, is unambiguously written A ∩ B ∩ C ∩ D.
Inside a universe U one may define the complement Ac of A to be the set of all elements of U not in A. Now the intersection of A and B may be written as the complement of the union of their complements, derived easily from De Morgan's laws:
A ∩ B = (Ac ∪ Bc)c
We say that A intersects (meets) B if A intersects B at some element. A intersects B if their intersection is inhabited. For example, the sets {1, 2} and {3, 4} are disjoint, while the set of even numbers intersects the set of multiples of 3 at the multiples of 6.