Ch.3 Solving Inequalities

3.5  Working with Sets Template

Roster Form – lists the elements of a set within braces { }

·  Set containing 1 & 2: {1, 2}

·  Set of multiples of 2: {…}2, 4, 6, 8,

Set Builder Notation – describes the properties an element must have to be included in a set.

·  Set of multiples of 2: {x | x is a multiple of 2}

Ø  Read as “the set of all real numbers x, such that x is a multiple of 2”

Ex.1: Write each set in roster form and set builder notation.

a.  T is the set of natural numbers that are less than 6

b.  N is the set of even natural numbers that are less than or equal to 12.

Ex.2: Write the solution of the inequality in set builder notation.

a.
-5x + 7 < 17 / b.
9 – 4n > 21

Empty Set (Null Set) – contains no elements { }

Ex.3: Complete.

a.  What are the subsets of the set ?

Empty set: 1 element sets: Original set:

Subsets:

b.  What are the subsets of the set ?

Empty set: 1 element sets: 2 element sets:

Original set: Subsets:

c.  Let and .

Is ? ( mean “subset”) Explain your reasoning.

Universal Set – the largest set you are using, denoted by U

Complement of a Set – the set of all elements in the universal set that are not in the set. You denote the complement of A by A´

Ex.4: Write the complement of set A in roster form.

a.  Universal set U = {months of the year} and set A = {months with exactly 31 days}

b.  Universal set U = {days of the week}, set A = {days with the letter T}

HW: pg.213 9-18,21,22,25-29,35-41