Lesson 2 1 Basic Set Concepts A set

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 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 • The set of Natural numbers N = {1, 2, 3, 4 ……} {1, 2, 3, …. }

• 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