14-1 sets warm up warm up problem of the day problem of the day lesson presentation lesson...
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14-1 Sets
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
Warm UpFill in each blank.
1. A ________ is a number that can be expressed in the form , where n and d are integers and d ≠ 0. 2. The set of _________ consists of the set of rational numbers and the set of irrational numbers.3. The set of _________ consists of the set of counting numbers, their opposites, and zero.
rational number
real numbers
14-1 Sets
Pre-Algebra
nd
integers
Problem of the Day
Use a traditional clock face to determine the next three terms in the following sequence: 1, 6, 11, 4, 9, . . .
2, 7, 12
Pre-Algebra
14-1 Sets
Learn to understand mathematical sets and set notation.
Pre-Algebra
14-1 Sets
Vocabulary
setelementsubsetfinite setinfinite set
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Pre-Algebra
14-1 Sets
Pre-Algebra
A set is a collection of objects, called elements. Elements of a set can be defined in two ways: roster notation and set-builder notation.
14-1 Sets
Pre-Algebra
Set Roster Notation Set-Builder Notation
{x|x is an even counting number}Read as “the set of all x such that x is an even counting number.”
Even countingnumbers
{2, 4, 6, 8, 10, …}
{Huron, Ontario,Michigan, Erie,Superior}
Great Lakes{x|x is one of the Great Lakes}
14-1 Sets
Pre-Algebra
The symbol is read as “is an element of.” Read the statement 3 {odd numbers} as “3 is an element of the set of odd numbers.” The symbol is read as “is not an element of.” Read the statement 2 {odd numbers} as “2 is not an element of the set of odd numbers.”
Think of the element symbol as the letter e.
Helpful Hint
14-1 Sets
Additional Example 1: Identifying Elements of a Set
Pre-Algebra
Insert or to make each statement true.
A. 4 {even integers}
4 {even integers}
B. shoes {furniture}
shoes {furniture}
C. rhombus {quadrilaterals}
rhombus {quadrilaterals}
4 is an even integer.
Shoes are not furniture.
A rhombus is a quadrilateral.
14-1 Sets
Try This: Example 1
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A. 3 {odd integers}
3 {odd integers}
B. shirts {coats}
shirts {coats}
C. square {rectangles}
square {rectangles}
3 is an odd integer.
Shirts are not coats.
A square is a rectangle.
Pre-Algebra
Insert or to make each statement true.
14-1 Sets
Pre-Algebra
Set A is a subset of set B if every elementin A is also in B. The symbol is read as“is a subset of” and the symbol is readas “is not a subset of.”
14-1 Sets
Determine whether the first set is a subset of the second set. Use the correct symbol.
Additional Example 2: Identifying Subsets
Pre-Algebra
A. E = {even numbers} Q = {rational numbers}
Yes, E Q. Every even number is a rational number.
B. A = {1, 2, 3, 4} B = {3,4}
No, A B. 1 and 2 are not in thesecond set.
C. C = {squares} D = {rectangles}Yes, C D. All squares are rectangles.
14-1 Sets
Try This: Example 2
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Pre-Algebra
Determine whether the first set is a subset of the second set. Use the correct symbol.
A. R = {sandals} S = {shoes}
Sandals are a type of shoe.
B. B = {1, 2, 5, 7} C = {1, 2, 5, 8}
7 is not in the second set.
C. E = {circles} F = {ovals}
A circle is not an oval.
Yes, R S.
No, B C.
Yes, E F.
14-1 Sets
Pre-Algebra
A finite set contains a finite number of elements. An infinite set contains an infinite number of elements.
14-1 Sets
Tell whether each set is finite or infinite.
Additional Example 3: Identifying Finite and Infinite Sets
Pre-Algebra
A. {students in a school}
finite There are a specific numberof students in a school.
B. {points on a line segment}
infinite Between any two points there is always another point.
C. {multiples of 5}
infiniteAny number can be multipliedby 5.
14-1 Sets
Try This: Example 3
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Pre-Algebra
Tell whether each set is finite or infinite.
A. {hairs on your head}
finite There are a specific numberof hairs on a person’s head.
B. {whole numbers between 1 and 10}
finite There are exactly 8 numbers in the set.
C. {real numbers between 1 and 10}infinite There are an infinite number of real
numbers between any two numbers.
14-1 Sets
Lesson Quiz: Part 1
Insert or to make each statement true.
1. 0 {whole numbers}
2. – {integers}
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Pre-Algebra
12
Determine whether the first set is a subset of the second set. Use the correct symbol.
3. T = {counting numbers}
P = {prime numbers}
No; T P
4. A = {a, e, o} Z = {vowels}
Yes; A Z
14-1 Sets
Lesson Quiz: Part 2
Tell whether each set is finite or infinite.
5. {two-digit whole numbers}
6. {polygons}
infinite
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finite
Pre-Algebra
14-1 Sets