2.1 Set Concepts 49 15. The set of NASCAR drivers who have exceeded 300 mile per hour in a race Well defined 16. The set of the most interesting teachers at your school Not well defined In Exercises 17–22, determine whether each set is finite or infinite. 17. 2, 3, 5, 8,13, 21 { } Finite 18. The set of natural numbers between 1 and 1 trillion, inclusive Finite 19. The set of odd numbers greater than 25 Infinite 20. The set of fractions between 1 and 2 Infinite 21. The set of odd numbers greater than 15 Infinite 22. The set of apple trees in Gro-More Farms Orchards Finite In Exercises 23–38, express each set in roster form. You may need to use the Internet or some other reference source. 23. The set of states in the United States whose names begin with the letter H {Hawaii} 24. The set of months whose names begin with the letter J {January, June, July} 25. The set of natural numbers less than 100 1, 2, 3, 4, , 99 { } … 26. The set of natural numbers less than or equal to 50 1, 2, 3, 4, , 50 { } … 27. The set of natural numbers greater than or equal to 10 { }… 10, 11, 12, 13, 28. The set of natural numbers greater than 17 { }… 18, 19, 20, 21, 29. The set of natural numbers between 5 and 100, inclusive 5, 6, 7,8, , 100 { } … 30. The set of natural numbers between 100 and 1000, inclusive 100, 101, 102,103, , 1000 { } … 31. = | ∈ ≤ < E x x N x { and 14 85} E 14, 15, 16, 17, , 84 { } = … 32. = | ∈ B x x N x { and is even} B 2, 4, 6, 8, { } = … 33. = | − = D x x { 7 3} { } 10 34. = | + = C x x { 6 10} { } = C 4 35. The set of natural number solutions to the equation + = x 2 0 { } or ∅ 36. The set of natural number solutions to the equation + = x 5 2 { } or ∅ 37. The set of football players over the age of 70 who are still playing in the National Football League { } or ∅ 38. The set of states in the United States that have a common border with Alaska { } or ∅ In Exercises 39– 48, express each set in set-builder notation. 39. { } = B 7, 8, 9, 10, 11, 12, 13, 14 = | ∈ < < B x x N x { and 6 15} or = | ∈ ≤ ≤ B x x N x { and 7 14} { } = A = < A x { | x N∈ and 10} or = ≤ A x { | x N∈ and 9} C { } 3, 6, 9, 12, = = C x { | x N∈ and is a multiple of 3} D { } 5, 10, 15, 20, = = D x { | x N∈ and is a multiple of 5} 100 and 400, ≤ x ≤ { a | ∈ x N d100 400} 12. ≥ x { a | ∈ x N d 12} E = E x { | x N∈ and is odd} A = A { | x is Independence Day} C = | C = x { is February} F {15, 16, 17, , 100} = … = ≤ ≤ F x { | x N∈ and 15 100} or = < < F x { | x N∈ and 14 101} A { } 1, 2,3, 4, 5,6, 7 = Set A is the set of natural numbers less than or equal to 7. D { } 3, 6, 9, 12, 15, 18, … = Set D is the set of natural numbers that are multiples of 3. { } V = Set V is the set of vowels in the English alphabet. = D { } Set D is the set of months of the year. T {oak, maple, elm, pine, } = {oak, maple, elm, pine, Set T is the set of species of trees. = ≤ E x { | x N∈ and 4 1 ≤ < 1} Set E is the set of natural numbers greater than or equal to 4 and less than 11. = S { } Set S is the set of seasons. C Africa, Antarctica, Asia, Europe, Australia, { = NorthAmerica, South America} Set C is the set of continents on Earth. m { } { } ∈} False; { } is a set, and not an element of the set. { } ∈ b True { } ∈ h False; h is not an element of the set. { } ∈ February True Gentoo Multimedia Limited/ Shutterstock
RkJQdWJsaXNoZXIy NjM5ODQ=