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. {1, 3, 5, 7, 9} and {1, 5, 9, 3, 7} {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 {1, 2, 3, 4, 5} and {a, e, i, o, u} {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. {1, 2, 3} {a, b, c, d} Formula:

Example 4: Subset/Not A Subset {2, 3, 7} ______{1, 2, 3, 4, 5, 6, 7} {-4, 0, 4} ______{-4, -3, -2, -1, 1, 3, 4} {x/x is a dog} ______{x/x is a pure bred dog}

Example 5: Proper Subsets List all the Proper Subsets. {1, 3, 4, 7, 9} {a, c, e, g} Formula:

Section 1.4 Assignment Classwork: Homework: 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: {1, 2, 3, 4, 5} List all the three element subsets: {a, b, c, d, e, f}

Example 7: Find a set that is equal to V. Student Major Class Rank GPA 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). Student Major Class Rank GPA Activities Taylor Math Junior 3.54 Drama Nicole Physics Senior 3.20 Soccer William Sophomore 2.43 Football Ed History 3.15 Band Jonathan English Freshman 2.6 Cynthia Art 1.9 Newspaper Terry Chemistry 3.74 Mary 2.83 Find a set that is equal to V.

Example 8: 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). Student Major Class Rank GPA Activities Taylor Math Junior 3.54 Drama Nicole Physics Senior 3.20 Soccer William Sophomore 2.43 Football Ed History 3.15 Band Jonathan English Freshman 2.6 Cynthia Art 1.9 Newspaper Terry Chemistry 3.74 Mary 2.83 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: Homework: 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: