14-1 Sets Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation Pre-Algebra

Warm Up Fill in each blank. 1. A ________ is a number that can be expressed in the form, where n and d are integers and d ≠ 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 ndnd 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 set element subset finite set infinite set Insert Lesson Title Here 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 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 counting numbers {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 Sets

Try This: Example 1 Insert Lesson Title Here 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 Sets

Pre-Algebra Set A is a subset of set B if every element in A is also in B. The symbol  is read as “is a subset of” and the symbol  is read as “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 the second set. C. C = {squares} D = {rectangles} Yes, C  D. All squares are rectangles Sets

Try This: Example 2 Insert Lesson Title Here 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 Sets

Pre-Algebra A finite set contains a finite number of elements. An infinite set contains an infinite number of elements 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 number of students in a school. B. {points on a line segment} infinite Between any two points there is always another point. C. {multiples of 5} infinite Any number can be multiplied by Sets

Try This: Example 3 Insert Lesson Title Here Pre-Algebra Tell whether each set is finite or infinite. A. {hairs on your head} finite There are a specific number of 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 Sets

Lesson Quiz: Part 1 Insert  or  to make each statement true {whole numbers} 2. – {integers} Insert Lesson Title Here Pre-Algebra  1212  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 Insert Lesson Title Here finite Pre-Algebra 14-1 Sets