Sure, let's go through the solution step by step.
### Given Information:
1. Correct Answers: C for question 1, B for question 2, A for question 3.
2. Student Answers:
- Student 1: {C, A, C}
- Student 2: {C, B, B}
- Student 3: {C, B, C}
- Student 4: {B, A}
- Student 5: {C, A, A}
### Sets Defined:
- Set 1: Students who answered C for question 1.
- Set 2: Students who answered B for question 2.
- Set 3: Students who answered A for question 3.
From the students' answers:
- Set 1: {1, 2, 3, 5}
- Set 2: {2, 3}
- Set 3: {5}
### a. [tex]\( \text{Set } 1 \cap \text{ Set 2} \)[/tex]
Intersection of Set 1 and Set 2 is the set of students who answered 'C' for question 1 and 'B' for question 2.
- Set 1: {1, 2, 3, 5}
- Set 2: {2, 3}
Intersection: {2, 3}
### Answer: {2, 3}
### b. [tex]\( \text{Set } 2 \cup \text{ Set 3} \)[/tex]
Union of Set 2 and Set 3 is the set of students who answered 'B' for question 2 or 'A' for question 3.
- Set 2: {2, 3}
- Set 3: {5}
Union: {2, 3, 5}
### Answer: {2, 3, 5}
### c. The Complement of Set 1
The complement of Set 1 is the set of students who did not answer 'C' for question 1.
- Set of all students: {1, 2, 3, 4, 5}
- Set 1: {1, 2, 3, 5}
Complement of Set 1: {4}
### Answer: {4}
### Context Explanation:
- Set 1 [tex]\(\cap\)[/tex] Set 2: Represents the students (Student 2 and Student 3) who answered 'C' for question 1 and 'B' for question 2.
- Set 2 [tex]\(\cup\)[/tex] Set 3: Represents the students (Student 2, Student 3, and Student 5) who answered 'B' for question 2 or 'A' for question 3.
- Complement of Set 1: Represents the students (Student 4) who did not answer 'C' for question 1.
By understanding these sets and their relationships, Mr. Montes can analyze the patterns in students' responses and identify common trends or areas where students may need additional help.
