## Chapter 1: Sets

**CHAPTER WRAP-UP**

1. Let the students do the exercises under the following components: Chapter Output (page 34), Chapter Challenger (page 35), Reflective Learning (page 37), and Chapter Assessment (pages 38–40).

2. Let the students state and discuss what they learned in the chapter and how they will apply what they learned. Guide them to form the chapter’s big idea.

2. Let the students state and discuss what they learned in the chapter and how they will apply what they learned. Guide them to form the chapter’s big idea.

**CULMINATION/TRANSFER**

The performance task will be in the form of a collection of at least five examples that illustrate set relations and operations: universal set, empty set, subset of a set, complement of a set, union of sets, intersection of sets, and set difference. The performance task will be assessed based on the following criteria in the rubric given on the next page.

• number of correct examples and descriptions

• relevance to everyday living

• neatness and organization

• number of correct examples and descriptions

• relevance to everyday living

• neatness and organization

**ANSWER KEY TO CHAPTER OUTPUT**

**ANSWER KEY TO CHAPTER OUTPUT**

1. Recall that for the type of problem given, it is only the cardinality of the set that you write in the region represented by the set in the Venn diagram. The aim is to determine the number of students who can play both badminton and table tennis but not volleyball. This is obtained by doing the following sequence of steps.

Let the sets be

B = set of students who can play badminton,

V = set of students who can play volleyball, and

T = set of students who can play table tennis.

You start by writing the cardinality of the region B ∩ V ∩ T. Since this set represents the set of students who can play all three games, you write 8 in the region as shown in the figure on the left below. Since 13 students can play both badminton and volleyball, the cardinality of the set B ∩ V is 13. Of these, 8 can also play table tennis. Thus, 13 – 8 = 5 is the number of students who can play badminton and volleyball but not table tennis, so write 5 in the region (B ∩ V) – T as shown in the middle figure below. Similarly, you obtain 11 – 8 = 3 as the number of students who can play volleyball and table tennis but not badminton as shown in the figure on the right below.

Let the sets be

B = set of students who can play badminton,

V = set of students who can play volleyball, and

T = set of students who can play table tennis.

You start by writing the cardinality of the region B ∩ V ∩ T. Since this set represents the set of students who can play all three games, you write 8 in the region as shown in the figure on the left below. Since 13 students can play both badminton and volleyball, the cardinality of the set B ∩ V is 13. Of these, 8 can also play table tennis. Thus, 13 – 8 = 5 is the number of students who can play badminton and volleyball but not table tennis, so write 5 in the region (B ∩ V) – T as shown in the middle figure below. Similarly, you obtain 11 – 8 = 3 as the number of students who can play volleyball and table tennis but not badminton as shown in the figure on the right below.

Since eight students can only play table tennis, you write 8 in the region T – (B ∪ V) as shown in the left figure below. Since 23 students play volleyball, and of these 3 + 5 + 8 = 16 are already accounted for in the Venn diagram, only 23 – 16 = 7 should be written in the region V – (B ∪ T).

See the middle figure below. Since 10 students can only play badminton, you write 10 in the region B – (V ∪ T). Refer to the figure on the right below.

See the middle figure below. Since 10 students can only play badminton, you write 10 in the region B – (V ∪ T). Refer to the figure on the right below.

The problem asks for the number of students who can play both badminton and table tennis but not volleyball. This is the cardinality of the region shaded in the right figure above. To determine this number, recall that each student in the class can play at least one of the three sports. Since there are 50 students in the class, the number of students who can play both badminton and table tennis but not volleyball is 50 – (8 + 5 + 3 + 8 + 7 + 10) = 50 – 41 = 9.

2. Since of the 22 members of the Science Club in the class, 17 are members of the Science Club only, it means that there are 22 – 17 = 5 Science Club members who are also Math Club members. From the assumption, there are also 5 students who are not members of any of the two clubs. Thus, you get the following:

a. There are (23 + 17) + 5 = 45 students in the class.

b. There are 5 students who are members of both clubs.

2. Since of the 22 members of the Science Club in the class, 17 are members of the Science Club only, it means that there are 22 – 17 = 5 Science Club members who are also Math Club members. From the assumption, there are also 5 students who are not members of any of the two clubs. Thus, you get the following:

a. There are (23 + 17) + 5 = 45 students in the class.

b. There are 5 students who are members of both clubs.

**DISCUSSION OF PERFORMANCE TASK**

1. a. Yes, the idea of sets play a role in film animation.

b. Images are constructed on computers as sets of points. Special effects or animations are created by moving these points using both algebra and geometry.

2. (Allow the pupils to discuss their answers.)

b. Images are constructed on computers as sets of points. Special effects or animations are created by moving these points using both algebra and geometry.

2. (Allow the pupils to discuss their answers.)

**ANSWER KEY TO REFLECTIVE LEARNING**

**Answer Key to Values Integration**

Answers may vary. Below is a sample answer.

Along with the mathematical ideas and concepts, I have learned the value of

Along with the mathematical ideas and concepts, I have learned the value of

__grouping things__through__sets__.**ANSWER KEY TO CHAPTER ASSESSMENT**

1. b
2. c 3. c 4. d 5. a 6. c 7. c 8. c 9. c 10. d |
11. a
12. c 13. a 14. b 15. a 16. d 17. b 18. d 19. d 20. c |