The Complete Discrete Math: Sets and Venn Diagrams Course

Explore singleton sets, their cardinality, and how to count elements using set notation like |M| = 1 in simple examples.

Explore finite sets and their cardinality, defined by a definite number of elements you can count, illustrated with D = {1,2,3} and A = {A,B,C}.

Explore infinite sets, where the number of elements is endless and unknown. The sequence y = 1, 2, 3 with ellipsis shows it continues without an end; cardinality remains unknown.

Define equal sets as having the same elements, regardless of order or repetition, and demonstrate equality with examples where two sets share exactly those elements.

Explore the null or empty set, its cardinality zero, and standard notation using curly brackets and the phi symbol, with examples distinguishing empty from not empty sets.

Explore subsets and the subset relation with examples like orange, apples, and pineapples, and distinguish the subset symbol from the not-subset symbol (with a stroke) and verify containment by elements.

Explains proper and improper subsets using a universal set and an example, comparing cardinalities and elements to show when one set is contained in another.

Demonstrate that sets R and S are equivalent when they share the same cardinality, illustrated by both having three elements.

This lecture defines the power set as all subsets, including the empty set, and shows that the cardinality equals two to the power of n.

Define the universal set as the set of all elements under consideration, or the universe, and show that every set is a subset of this universe.

Identify the universal set for several examples—odd numbers, polygon shapes, clothing categories, and names—demonstrating how to determine a universal set from different sets.

Classify sets as finite or infinite by counting elements, using examples like finite sets of african schools and W = {1,2,3} versus the fractions between one and two.

Explain basic set concepts using examples: elements inside braces vs empty sets, nonempty sets, prime numbers between eight and ten, and months with initials.

Identify natural numbers as the positive integers represented by N, starting at one. Show that the set 1,2,3,4,5,... extends indefinitely.

Identify the set of integers Z as all negative, zero, and positive numbers, illustrated with ellipses showing the sequence continues indefinitely.

Rational numbers are numbers that can be expressed as a ratio of two integers, with the denominator not equal to zero, including all integers.

Identify irrational numbers as the set of numbers not representable as a ratio of two integers, distinct from rational numbers. Explain the notation used to denote this set.

Real numbers form the set R, encompassing both rational numbers, expressible as a ratio, and irrational numbers, not expressible as a ratio.

Represent the universal set as a rectangle and depict subsets as circles inside it to show how elements belong to different sets.

This example demonstrates representing a universal set with a rectangle and two sets in circles, showing how days like Tuesday and Thursday belong to X or Y, with others outside.

Construct a Venn diagram by representing the universal set as a rectangle and a subset as a circle, placing elements inside and outside to show membership.

Illustrate the universal set with two subsets, E and D, where E = {3,5} is inside D = {0,3,5,8}. Show elements unique to each set and those outside both.

Learn how to compute the union of sets X and Y (X ∪ Y) by listing elements from either set, using Venn diagrams to show union, intersection, and subset relationships.

Explore the union properties with X and Y, showing commutativity X∪Y = Y∪X, subset intuition X⊆Y ⇒ X∪Y = Y, and associativity X∪Y∪Z = (X∪Y)∪Z = X∪(Y∪Z).

Learn to construct and interpret the union of sets C and D with a Venn diagram, identify the intersection elements such as orange, and shade the union.

Demonstrate the union of two disjoint sets M and N in the universal set, listing M = {1,3,4,5} and N = {6,7}, with a Venn diagram showing no intersection.

Illustrates constructing sets from inequalities by listing elements, such as 6–10 and 7–12 and 4–12, and shows how to form the union of three sets by combining their elements.

Explore the intersection of two sets, the elements common to both, shown with the symbol ∩ and a Venn diagram, illustrated by P = {1,2,3} and Q = {2,4,5}.

Identify the intersection of X and Y on a Venn diagram by listing common elements (8 and 9), drawing two overlapping circles, and shading the intersection region.

Explore disjoint sets by comparing vowels and consonants in the English alphabet, showing empty intersection and how a Venn diagram represents non-overlapping sets within a universal set.

Explore the properties of intersection for sets P, Q, and R, including commutativity and associativity, and prove distributive laws with Venn diagrams and subset relations.

Explore sets, universal and subset relations, and the intersection in a Venn diagram, using G and H to illustrate how G and H intersect in {3,5,7}.

explores computing intersections and unions of sets K, L, and M from even numbers 2–24, identifying elements common to pairs and all three.

Explore the complements of a set within the universal set, using notation Y' and Venn diagrams to identify elements not in Y.

Explore complements in the universal set by identifying elements not in given sets, and work through an example to find complements of A, B, C, and others.

Compute X intersect Y and its complement within the universal set, using X and Y and their primes, and visualize with Venn diagrams while applying Morgan's law.

Explore relative complement (difference) of sets by computing A minus B, identifying elements in A not in B, using Venn diagrams and universal sets to visualize.

Explore set operations with C and D, compute C minus D and minus C, and identify odd numbers between four and ten to reveal C as an empty set.

Develop fluency with two-set problems by using venn diagrams to identify A and B regions, including A ∩ B, A ∪ B, A only, B only, and complements.

Solve a two-set problem with a Venn diagram to determine counts for apples, mangoes, both, only, and neither among 40 people.

Determine math and physics enrollment in a class of 20 using a Venn diagram. Find that 12 take math, with 5 math-only and 7 math-and-physics, and 3 take neither.

Explore three-set problems with a three-circle Venn diagram of X, Y, and Z. Identify intersections X∩Y, Y∩Z, X∩Z, and X∩Y∩Z, and the union X∪Y∪Z with its complement.

Explore calculating the cardinality of three sets P, Q, and R by analyzing elements, intersections, and the union, and learn to determine P ∪ Q ∪ R, P ∩ Q.

Explore a three-set Venn diagram approach to discrete math, calculating union and intersection for maths, music, and visual arts in the class of 160.

Apply a three-set Venn diagram to a 40-female survey to compute the triple intersection of gowns, blouses, and socks, finding X = 3.

We conclude this course and invite you to drop questions in the questions section. Visit the geometry course link below or search for angles and polygons made ridiculously easy.