Use Venn diagrams to solve problems

Learning Objectives Interpret and label a two-set and three-set Venn diagram from a word problem. Calculate the number of elements in the union and intersection of two or three sets. Determine the number of elements belonging to exactly one set, exactly two sets, or all three sets. Find the number of elements in the complement of a set or the complement of a union of sets. Solve for an unknown value within a Venn diagram problem using algebraic expressions. Apply the Principle of Inclusion-Exclusion to solve problems and verify solutions. Ever wonder how many of your classmates are on both TikTok and Instagram, and how many use neither? 🤔 Venn diagrams are the perfect visual tool to solve exactly this kind of puzzle! This tutorial will teach you how to translate informatio...

TermDefinitionExample SetA collection of distinct objects or elements, usually enclosed in curly braces {}.The set of primary colors is {red, yellow, blue}. Universal Set (U)The set containing all possible elements being considered in a particular problem. In a Venn diagram, it is represented by the rectangle.If discussing students in a specific classroom, the universal set U is all the students in that classroom. Intersection (A ∩ B)The set of elements that are in BOTH set A AND set B. This is the overlapping region of the circles in a Venn diagram.If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A ∩ B = {3, 4}. Union (A ∪ B)The set of elements that are in set A OR set B (or in both). This includes all regions of the circles.If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}....

Principle of Inclusion-Exclusion (Two Sets) n(A ∪ B) = n(A) + n(B) - n(A ∩ B) To find the total number of elements in the union of two sets, add the cardinalities of each set and then subtract the cardinality of their intersection. This corrects for the elements that were counted twice. Principle of Inclusion-Exclusion (Three Sets) n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C) For three sets, you add the cardinalities of the individual sets, subtract the cardinalities of all the two-set intersections, and finally add back the cardinality of the three-set intersection. Complement Rule n(A') = n(U) - n(A) The number of elements not in set A is equal to the total number of elements in the universal set minus the number of element...