Set Theory Notes

Set Concepts. Set is a collection of elements. Elements are the items in a set. A set is well-defined if the elements can be clearly determined. Months of year, days of week, etc. list all elements of a set is a roster. Braces are used to indicate a set. Natural numbers are called the counting numbers. Ellipsis… whole numbers W. Integers I. Inclusive means including the limits. Inbetween two certain points or numbers. Set builder notation. Set a is the set of all x such that x is a natural number less than ten. A set that contains no elements is the empty set. Zero with lines through it or empty braces. Universal set contains all the elements. Finite set has specific numb. Of elements. Infinite set has no limit. Equal if contain exactly the same elements. Cardinal number tells number of elements in a set.

Subset has the line under it. Everything in A is also in B. Proper subset no line under it. If everything in A is also in B and set a isn’t equal to set b. set b must contain something that A does not. The empty set is a subset of every set! A set will have 2^n subsets, where n is the number of elements of the set.

Sets a and b are disjoint when they have no common elements. Regions of 2 set Venn diagram. I, II, III, IV. The Complement of set a is the set of the elements in the universal set that aren’t in a. Intersection. Upside down U. in both a AND b. Union. A U. in either a OR b.

3 sets venn diagrams. DESCRIBE what each region means. Start with region V, then II, IV, VI. Easiest way.

Applications of sets. Make venn diagrams to solve problems. Don’t forget to put how many aren’t in the circles!