Professor is running behind today. At least the room was unlocked, so we can sit down.9:18 — Prof is here, class is ready to start. Just rubbed my nose and had an allergy attack. I sincerely hopethis isn’t a recurrance of the coat thing. I hung that coat up in the closet, and this shirt was also hanging in there. I suppose it’s possible that whatever is on the coat has spread to everything else in the closet, but if so, that’s really bad news for me. It might also mean something in the closet was the root cause all along, which isn’t any better.
Equality of sets means that two sets contain the same elements. No set contains elements the other set does not.
A subset is a set which contains only elements that are contained in another set. Equal sets are subsets of each other. A proper subset is a subset which is not equal to its parent set. The null set is a subset of all sets.
The Universal Set U is defined as the set consisting of all elements under consideration.
Venn Diagrams are useful tools for visualizing set relationships. The universal set is drawn as a rectangle. Other sets are represented as circles within that rectangle. If sets have shared subsets, the circles are drawn as overlapping.
The union of two sets is the set containing all elements of both sets.
The intersection of two sets is the set of elements shared by those two sets. If the intersection of two sets is a null or empty set, the sets are called disjoint sets.
The complement of a set is the set containing all elements of U, the universal set, not contained in that set. The union of a set and its complement is equal to the universal set.
De Morgan’s properties are two relationships which are always true for sets. De Morgan’s first property is that the complement of the union of two sets is equal to the intersection of the complements of each set. De Morgan’s second property is that the complement of the intersection of two sets is equal to the union of the complements of each set.
For a set A, the number of elements in that set is defined as c(A).
The counting formula is a formula for determining the number of elements in the union of two sets. The formula states that the count of elements in the union of two sets is equal to the number of elements in the first set, plus the number of elements in the second set, minus the number of elements in the intersection of the two sets. The number of elements in the intersection must be subtracted to prevent those element from being counted twice.