1. PROBLEMS INVOLVING SETS

2. Choose the correct set notation formula for each Venn diagram.B
(A ∪ B)’ A ∩ B A’ ∩ B A ∪ B
A’ (A ∩ B)’

3. Shade the region in the Venn diagram that is described by the set notation formula.
A ∩ B’ B’ U A B
(A ∩ B)’

4. Think About This
Given 3 sets, what set notation formula would describe the shaded region?

5. WORD PROBLEMS

6. 1. A group of 25 high school students were asked whether they use either Facebook or Twitter or both. Fifteen of these students use Facebook and twelve use Twitter. a. How many use Facebook only? b. How many use Twitter only? c. How many use both social networking sites?

7. Solution: Let S1 = set of students who use Facebook only S2 = set of students who use both social networking sites S3 = set of students who use Twitter only The Venn diagram is shown below
FACEBOOK
TWITTER

8. FACEBOOK
TWITTER
FACEBOOK
TWITTER

9. FACEBOOK
TWITTER S1 S2 S3
Finding the elements in each region: n(S1) + n( S2) + n(S3) = 25 n(S1) + n( S2) + n(S3) = 25 n(S1) + n( S2) = 15 n( S2) + n(S3) = 12 ______________________ ______________________ n(S3) = 10 n(S1) = 13 But n( S2) + n(S3) = 12 _____________________ n( S2) = 2

10. U 13 2 10

11. In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. How many like both coffee and tea?

12. Solution: Let D1 = set of people who like cold drinks only D2 = set of people who like both cold and hot drinks D3 = set of people who like hot drinks only The Venn diagram is shown below
COLD DRINKS
HOT DRINKS

13. COLD DRINKS
HOT DRINKS
COLD DRINKS
HOT DRINKS

14. COLD DRINKS
HOT DRINKS D1 D2 D3
Finding the elements in each region: n(D1) + n(D2) + n(D3) = 60 n(D1) + n(D2) + n(D3) = 60 n(D1) + n( D2) = 27 n(D2) + n(D3) = 42 ______________________ ______________________ n(D3) = 33 n(D1) = 18 But n( D2) + n(D3) = 42 _____________________ n( D2) = 9

15. 18 9 33 U
COLD DRINKS
HOT DRINKS

16. Among the 70 kids in Barangay Magana, 53 like eating in Jollibee while 42 like eating in McDonalds. How many like eating both in Jollibee and in McDonalds? In Jollibee only? In McDonalds only?

17. Try This
A teacher announces that out of 35 students in class, 25 passed both the Math and Science tests, 30 passed the Math test, and 28 passed the Science test. How many students did not pass either the Math or Science test?

18. Exercises
1. In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak English only? How many can speak French only and how many can speak both English and French?

19. Exercises
2. In a class of 80 boys, there are 60 boys who play rugby and 35 play tennis. Use Venn diagrams to show how many boys play both the games? How many play rugby only and how many play tennis only? 

20. A survey asked 100 students whether they play volleyball or basketball
A survey asked 100 students whether they play volleyball or basketball. Eighteen students play both basketball and volleyball, 41 play basketball, and 51 play volleyball.
How many play volleyball only?
How many play basketball only?
How many students do not play either sports?

21. into swimming but not basketball? Into both swimming and basketball?
The Venn diagram shows student involvement in two sports – swimming and basketball. If 100 students were surveyed, how many students were
into swimming but not basketball?
Into both swimming and basketball?
Into either swimming or basketball?
neither into swimming nor basketball? U S B 15 20 30

22. dancing but not singing? either singing or dancing?
140 students were surveyed. The Venn diagram shows the number of students who enjoy singing/or dancing. How many students enjoy
dancing but not singing?
either singing or dancing?
both singing and dancing?
neither singing nor dancing? U S D 43 55 32

23. WORD PROBLEMS INVOLVING 3 SETS

24. COPY!
A group of 50 students went in a tour in Palawan province. Out of the 50 students, 24 joined the trip to Coron; 18 went to Tubbataha Reef; 20 visited El Nido; 12 made a trip to Coron and Tubbataha Reef; 15 saw Tubbataha Reef and El Nido; 11 made a trip to Coron and El Nido and 10 saw the three tourist spots. a. How many of the students went to Coron only? b. How many of the students went to Tubbataha Reef only? c. How many joined the El Nido trip only? d. How many did not go to any of the tourist spots?

25. CORON
EL NIDO
TUBBATAHA REEF U
a. How many of the students went to Coron only? b. How many of the students went to Tubbataha Reef only? c. How many joined the El Nido trip only? d. How many did not go to any of the tourist spots?

26. Superburger sells hamburgers with the choice of ketchup, mustard and relish. One day they sold 256 hamburgers; 140 had mustard, 140 had ketchup, 84 had ketchup and relish, 62 had mustard but no relish, 68 had ketchup and mustard, 38 had all three condiments and 20 had none. (a) The number sold with relish only is? (b)The number sold with no relish is?
Circle K: Burgers with Ketchup Circle R: Burgers with Relish Circle M: Burgers with Mustard Like so: U

27. A survey of 100 students revealed that 30 played tennis, 25 played golf, 40 played baseball. 10 played tennis and golf, 15 played golf and baseball, 20 played tennis and baseball, and 8 played all three.
How many played tennis only?
How many played golf only?
How many played baseball only?
How many did not play any of the three?
GOLF
TENNIS
BASEBALL U

28. 100 students were interviewed 28 took PE, 31 took BIO, 42 took ENG, 9 took PE and BIO, 10 took PE and ENG, 6 took BIO and ENG, 4 took all three subjects. a) How many students took none of the three subjects? b) How many students took PE but not BIO or ENG? c) How many students took BIO and PE but not ENG? PE
ENG
BIO U

29. 90 students went to a school carnival
90 students went to a school carnival. 3 had a hamburger, soft drink and ice-cream. 24 had hamburgers. 5 had a hamburger and a soft drink. 33 had soft drinks. 10 had a soft drink and ice-cream. 38 had ice-cream. 8 had a hamburger and ice-cream. How many had nothing?
HAMBURGER
SOFT DRINK
ICE CREAM U

30. A class has 175 students. The following is the description of students studying one or more of the following subjects in this class. Mathematics 100, Physics 70, Chemistry 46, Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18.
How many students are
enrolled in Mathematics only?
B. Physics only?
Chemistry only?
None of the three subjects?
Mathematics
Physics
Chemistry U

31. 100 students went to a zoo. 76 went to see the lion
100 students went to a zoo. 76 went to see the lion. 48 went to see the giraffes and 43 went to see the elephants. 42 saw the lion and the giraffes. 14 went to see the giraffes and the elephants. 31 went to see the lion and the elephants. 10 students saw all three.
A. How many saw the lion only?
Elephants only?
Giraffes only?
None of the three?
LION
GIRAFFES
ELEPHANTS U

32. EXAMPLES
Fifty people are asked about the pets they keep at home. The Venn diagram shows the results.
Let D = {people who have dogs}
F = {people who have fish}, and
C = {people who have cats}.
How many people have
dogs?
dogs and fish?
dogs or cats?
fish and cats but not dogs?
dogs or fish but not cats?
all three?
neither one of the three? U D F 1 12 3 C

33. TRY THIS
One hundred (100) people were surveyed. Suppose B = people who like beaches}, M = {people who like mountains}, and
C = {people who like big cities}.
How many people like
big cities only?
mountains or beaches?
mountains and beaches
but not big cities?
cities or beaches but
not mountains?
all three?
neither of the three? U B M 10 21 8 C

34. 1. In a survey of 200 students of a school it was found that 120 study mathematics, 90 study physics and 70 study chemistry, 40 study mathematics and physics, 30 study physics and chemistry, 50 study chemistry and mathematics and 20 study none of these subjects. Find the number of students who study all three subjects. 

35. 1. In a survey of 279 college students, it is found that 68 like brussels sprouts, 90 like a broccoli, 57 like cauliflower, 29 like both Brussels sprouts and broccoli, 25 like both Brussels sprouts and cauliflower, 24 like both broccoli and cauliflower, and 14 of the students like all three vegetables. a. How many like brussel sprouts only? b. How many like broccoli only? c. How many like cauliflower only? d. How many do not like any of the three vegetables?

36. One hundred (100) students were surveyed on their preference in movies.
Let U = {all students}
H = {students who like horror films}
F = {students who like fantasy}
C = {students who like comedy}.
Find the number of students
who like comedy only.
who like horror and fantasy.
who like horror or fantasy.
who like horror and comedy
but not fantasy.
e. who do not like horror.
f. who like horror, fantasy, and
comedy.
g. who do not like any of these
three? U H C 10 20 F

37. TUMAHIMIK PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

38. ISULAT SA ½ CROSSWISE ANG PANGALAN NG GROUP PATI MGA KASAMA SA GRUPO.
MAG-ISIP NG PANGALAN NG GROUP NINYO. KAILANGAN MAYROONG SALITANG MATH SA PANGALAN NG GRUPO HALIMBAWA, MATHAPANG
ISULAT SA ½ CROSSWISE ANG PANGALAN NG GROUP
PATI MGA KASAMA SA GRUPO.

39. HUWAG NG KOPYAHIN ANG PROBLEM. GUMAWA AGAD NG VENN DIAGRAM
HUWAG NG KOPYAHIN ANG PROBLEM. GUMAWA AGAD NG VENN DIAGRAM. YUNG MGA QUESTIONS LANG ANG KOPYAHIN.