SECTION 1.4

Comparing Sets

Objectives

Recognize equivalent sets.

Recognize equal sets.

Recognize subsets and use the notation .

Recognize proper subsets and use the notation .

Determine the number of subsets of a set.

Key Terms Equal: Set A is equal to Set B iff they contain exactly the

same elements, regardless of order or possible repetition of elements, symbolized by A = B.

Equivalent: sets are said to be equivalent if they contain the same number of elements, and the elements can be placed in a one-to-one correspondence.

Subset: Set A is a subset of Set B, symbolized by A B, iff all the elements of Set A are also elements of Set B.

Proper Subset: Set A is a proper subset of Set B, symbolized by A B, iff all the elements of Set A are elements of Set B and Set A ≠ Set B (Set B has to be larger).

**Special Note:

All equal sets are equivalent, but all equivalent sets are not equal.

Example 1: Equal Sets – exactly the same elements Decide whether each pair of sets is equal.

a. {1, 3, 5, 7, 9} and {1, 5, 9, 3, 7}

b. {x/x is a counting number between 5 and 19 inclusive}

{y/y is a rational number between 5 and 19 inclusive}

Example 2: Equivalent Sets – exactly the same number of elements Decide whether each set is equivalent

a. {1, 2, 3, 4, 5} and {a, e, i, o, u}

b. {x/x is a letter in the world tenacity} and {x/x is a letter in the word resolve}

Example 3: Subsets

List all the subsets.

a. {1, 2, 3}

b. {a, b, c, d}

Formula:

Example 4: Subset/Not A Subset

a. {2, 3, 7} ______{1, 2, 3, 4, 5, 6, 7}

b. {-4, 0, 4} ______{-4, -3, -2, -1, 1, 3, 4}

c. {x/x is a dog} ______{x/x is a pure bred dog}

Example 5: Proper Subsets

List all the Proper Subsets.

a. {1, 3, 4, 7, 9}

b. {a, c, e, g}

Formula:

Section 1.4 Assignment

Classwork: TB pg. 36/2 – 30 Even

Must write problems and show ALL answers to receive credit for this assignment.

Homework:

Example 6: Subsets

List all the two element subsets:

a. {1, 2, 3, 4, 5}

List all the three element subsets:

b. {a, b, c, d, e, f}

Example 7:

Student Major Class Rank

GPA Activities

Taylor Math Junior 3.54 Drama

Nicole Physics Senior 3.20 Soccer

William Math Sophomore 2.43 Football

Ed History Junior 3.15 Band

Jonathan English Freshman 2.6 Drama

Cynthia Art Freshman 1.9 Newspaper

Terry Chemistry Senior 3.74 Soccer

Mary English Sophomore 2.83 Band

Consider the following sets: U = (Upperclassmen); L = (Lowerclassmen); S (Science Majors); V (GPA above 3.0); A (Art Majors); T (Athletes); and D (involved in Drama).

Find a set that is equal to V.

Example 8:

Student Major Class Rank

GPA Activities

Taylor Math Junior 3.54 Drama

Nicole Physics Senior 3.20 Soccer

William Math Sophomore 2.43 Football

Ed History Junior 3.15 Band

Jonathan English Freshman 2.6 Drama

Cynthia Art Freshman 1.9 Newspaper

Terry Chemistry Senior 3.74 Soccer

Mary English Sophomore 2.83 Band

Consider the following sets: U = (Upperclassmen); L = (Lowerclassmen); S (Science Majors); V (GPA above 3.0); A (Art Majors); T (Athletes); and D (involved in Drama).

Find a set whose cardinal number is the largest of all the sets.

Example 9:

TB pg. 33/Example 3

Section 1.4 Assignments

Classwork: TB pg. 36/31 – 34, 39 – 46, and 51 and 52

Must write problems and show ALL answers to receive credit for this assignment.

Homework: