See Problem 3.

Draw a Venn diagram to represent the union and intersection of these sets.

22. The letters in the words ALGEBRA, GEOMETRY, and CALCULUS are represented by the sets V = { A , L , G , E , B , R } , W = { G , E , O , M , T , R , Y } , v equals left brace cap a comma cap l comma cap g comma cap e comma cap b comma cap r right brace comma w equals left brace cap g comma cap e comma cap o comma cap m comma cap t comma cap r comma cap y right brace comma  and X = { C , A , L , U , S } , x equals left brace cap c comma cap a comma cap l comma cap u comma cap s right brace comma  respectively.
23. Let E = { x | x e equals left brace x vertical line x  is a positive, composite number less than 10 } , F = { 1 , 2 , 4 , 5 , 6 , 8 , 9 } , 10 right brace comma f equals left brace 1 comma 2 comma 4 comma 5 comma 6 comma 8 comma 9 right brace comma  and G = { x | x g equals left brace x vertical line x  is a positive, even number less than or equal to 10}.
24. Let L = { A , B , C , 1 , 2 , 3 , horse , cow , pig } , M = { − 1 , 0 , 1 , B , Y , pig , duck , Δ } , l equals left brace cap a comma cap b comma cap c comma 1 comma 2 comma 3 comma , horse , comma cow comma pig right brace comma m equals left brace negative 1 comma 0 comma 1 comma cap b comma cap y comma pig comma , duck , comma cap delta right brace comma  and N = { C , 3 , duck , Δ } . n equals left brace cap c comma 3 comma , duck , comma cap delta right brace .

See Problem 4.

25. Camping Twenty-eight girls went camping. There were two main activities: volleyball and swimming. Fourteen girls went swimming, 5 participated in both activities, and 4 girls did neither. How many girls only played volleyball?
26. Winter Sports A ski shop owner surveys 200 people who ski or snowboard. If 196 people ski and 154 people do both activities, how many people snowboard?

See Problem 5.

Solve each inequality. Write the solutions as either the union or intersection of two sets.

27. | 3 x − 5 | < 14 vertical line 3 x minus 5 vertical line less than 14
28. − 6 < n + 7 ≤ 21 negative 6 less than n plus 7 less than or equal to 21
29. | 8 w − 1 | ≥ 7 vertical line 8 w minus 1 vertical line greater than or equal to 7
30. 3 ≤ | 5 d + 11 | 3 less than or equal to vertical line 5 d plus 11 vertical line
31. 2 | x − 7 | > 28 2 vertical line x minus 7 vertical line greater than 28
32. | 4.5 t − 1.5 | ≤ 12 vertical line 4.5 t minus 1.5 vertical line less than or equal to 12

B Apply

Find each union or intersection. Let W = { 5 , 6 , 7 , 8 } , X = { 3 , 6 , 9 } , Y = { 2 , 3 , 7 , 8 } , w equals left brace 5 comma 6 comma 7 comma 8 right brace comma x equals left brace 3 comma 6 comma 9 right brace comma y equals left brace 2 comma 3 comma 7 comma 8 right brace comma  and Z = { x | x z equals left brace x vertical line x  is an even whole number less than 10}.

33. W ∪ Y ∪ Z w union y union z
34. X ∩ Y ∩ Z x intersection y intersection z
35. W ∩ X ∩ Z w intersection x intersection z
36. Writing Let M = { x | x  is a multiple of  3 } m equals left brace x vertical line x . isamultipleof . 3 right brace  and N = { x | x  is a multiple of  5 } . n equals left brace x vertical line x . isamultipleof . 5 right brace .  Describe the intersection of M and N.
37. Think About a Plan Blood type is determined partly by which antigens a red blood cell has. An antigen is a protein on the surface of a red blood cell. Type A contains the A antigen. Type B contains the B antigen. Type AB contains both A and B antigens. Type O does not have any antigens. A hospital has 25 patients with the A antigen, 17 with the B antigen, 10 with the A and B antigens, and 30 without A or B antigens. How many patients are represented by the data?
    • How can a Venn diagram help you solve the problem?
    • What strategies can you use to complete the Venn diagram?
38. Sports In a survey of students about favorite sports, the results include 22 who like tennis, 25 who like football, 9 who like tennis and football, 17 who like tennis and baseball, 20 who like football and baseball, 6 who like all three sports, and 4 who like none of the sports. How many students like only tennis and football? How many students like only tennis and baseball? How many students like only baseball and football?
39. Reasoning Suppose A and B are sets such that A ⊆ B . eh subset of or equal to b .  What is true about A ∩ B ? eh intersection b question mark

Table of Contents