Lesson 2.1 Basic Set Concepts

A set is a collection of objects whose contents can be clearly determined. Elements, or members, - the objects in a set Capital letters are used to name sets. Methods to name sets: 1) word description 2) roster method 3) set builder notation Roster method lists all elements in braces { }

Write a word description for the set. L = {a, b, c, d, e} Set builder notation Lets express days of the week in s.b.n W = {x| x is a day of the week

Express in roster and set builder notation. M is the set of all months beginning with the letter M.

The symbol is used to indicate that an object is an element of a set. The empty set, or null set, contains no elements. Represented by { } or ø. {x|x is greater than 8 and less than 2 The symbol is used to indicate that an object is an element of a set.

True or false v {a, b, c … z ) -3 {1, 2, 3, ….} The set of Natural numbers N = {1,2,3,4 ……}

The number of elements in a set is called the cardinal number, or cardinality, of the set. L = {a,e,i,o,u} has cardinality of 5 Symbol n(L) is read “n of L.” Repeating Elements in a set does not add to the cardinality of a set.

If set A is equivalent to set B, then set A and B contain the same number of elements. n(A) = n(B) Example

If set A is equal to set B then, A and B contain exactly the same elements, regardless of order or possible repetition. A = B example

Finite set – has a definite number of elements Infinite set – doesn't have a set number of elements Examples