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Intersection of Sets (see Section 4): The union A [B of two sets A and B is characterized by the assertions x 2 A or x 2 B. The intersection A \ B of two sets A and B is characterized by the assertions x 2 A and x 2 B. More generally, given a non-empty set C of sets, the intersection D := ∩ C2C C is defined by the property that x 2 D if and ...
Determine the intersection ∩ of these two sets. There are no common numbers to both A and B, so the intersection is the empty set. = {1,3,5} and = {2,4, 6}. Determine the union ∪ of these two sets. The numbers that belong to either A or B, or both sets, are all the given numbers written from the smallest to the largest. So,
Understand what is meant by the intersection of two sets. Using proper notation for unions and intersections. The union of two sets A and B is a set that contains all of the elements found in Set A and all of the elements found in Set B, without duplicating any elements that are common to both sets.
We say that x is an element of/in a set A, written x 2 A, if it belongs in the set. We write x 62A if not. Example 1.1. For example 3 2 Z and 3:4 62Z. We can also explicitly list the elements in a set using fg notation. Example 1.2. Here are a few: f1; 2; 3; 4g contains four things, the numbers 1,2,3, and 4. fprimesg contains all the primes.
1.6. Operations on sets: union, intersection. We define several operations on sets. Let A and B be arbitrary sets. The union of A and B, written A ∪ B, is the set whose elements are just the elements of A or B or of both. In the predicate notation the definition is A ∪ B =def {x x ∈ A or x ∈ B} Examples. Let K = {a,b}, L = {c,d} and M ...
Intersection: Given two or more sets, A and B, the intersection of A and B is the set whose elements are common to both A and B . Notation: The intersection of two sets is given by ‘ AB ∩ ’.
The Joy of Sets Autumn 2011 The study of modern mathematics requires a basic familiarity with the notions and notation of set theory. For a rigorous treatment of set theory, you may wish to take Math 582, Introduction to Set Theory. What is a set? A colony of beavers, an unkindness of ravens, a murder of crows, a
