Tiêu đề 23 Venn Diagram and Set Theory.pdf ✅

A ⊕ B = {3, 4, 5, 6, ... } In worded problems, the set difference is used when the object is described with “but not.” The symmetric difference is used when the object is described with “exclusively or.” From the mangoes earlier, “Mangoes that are Indian but not yellow” = “Indian” \ “yellow” = green Indian mangoes “Mangoes that are yellow but not Indian” = “yellow” \ “Indian” = yellow mangoes of other varieties “Mangoes exclusively Indian or yellow” = “Indian” ⊕ “yellow” = green Indian mangoes or yellow mangoes of other varieties The complement of a set is another set containing elements not in the original set but in the universal. It is denoted by putting an apostrophe on the original set. For the earlier sets where A is the set of primes and B is the set of even numbers, A ′ = set of composite numbers B ′ = set of odd numbers From the definition of complement, A ′ = U \ A A ∪ A ′ = U A set with no elements is called a null set, denoted by ∅. Note that there are no common elements in a set and its complement. A ∩ A ′ = ∅ 3. Venn diagrams Venn diagrams are visual representations of multiple sets. The earlier set operations can be represented in Venn diagrams in the areas shaded below. Intersection of sets (A ∩ B): Union of sets (A ∪ B):
Set difference (A\B and B\A): Symmetric difference (A ⊕ B): Complement (A ′ and B ′ ): The Venn diagrams of three sets and four sets must be able to have a region for each possible combination of sets. The Venn diagrams of these sets are as shown: