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