Question

1. Write whether each of the following sets is well-defined or not.

1. The set of honest people
2. The set of even counting numbers
3. The set of prime numbers
4. The set of big people
5. The set of dedicated students

2. Write the elements and cardinality of the following sets:
1. Set M is the set of counting odd numbers less than ___
2. Set A is the set of months that start with the letter ___
3. Set T is the set of all factors of ___
4. Set H is the set of subjects you have in grade ___
5. Set I is the set of prime numbers between 1 and ___
6. Set S is the set of distinct letters from the word 'araling panlipunan'
7. Set F is the set of vowels from the word ___
8. Set U is the set of consonants from the word 'english'
9. Set N is the set of composite numbers from 11 to 20.

Answer 1

1. The set of honest people, big people, and dedicated students are not well-defined. The sets of even counting numbers and prime numbers are well-defined. 2. Set M: Counting odd numbers less than 10 (elements: 1, 3, 5, 7, 9). Set A: Months that start with the letter 'J' (elements: January, June, July). Set T: All factors of 10 (elements: 1, 2, 5, 10). Set H: Subjects you have in grade 7 (elements: Mathematics, English, Science, Social Studies). Set I: Prime numbers between 1 and 100 (elements: 2, 3, 5, 7, 11, ..., 97). Set S: Distinct letters from the word 'araling panlipunan' (elements: a, r, l, i, n, g, p, u). Set F: Vowels from the word 'example' (elements: a, e). Set U: Consonants from the word 'english' (elements: n, g, l, s, h). Set N: Composite numbers from 11 to 20 (elements: 12, 14, 15, 16, 18, 20).

Step-by-step explanation:

1. The set of honest people is not well-defined because honesty is subjective and can vary from person to person.
2. The set of even counting numbers is well-defined and can be represented as {2, 4, 6, 8, ...}.
3. The set of prime numbers is well-defined and can be represented as {2, 3, 5, 7, 11, ...}.
4. The set of big people is not well-defined because the term 'big' is vague and can have different interpretations.
5. The set of dedicated students is not well-defined because the term 'dedicated' is subjective and can vary for each individual.

1. Set M: Counting odd numbers less than 10. Elements: {1, 3, 5, 7, 9}. Cardinality: 5.
2. Set A: Months that start with the letter 'J'. Elements: {January, June, July}. Cardinality: 3.
3. Set T: All factors of 10. Elements: {1, 2, 5, 10}. Cardinality: 4.
4. Set H: Subjects you have in grade 7. Elements: {Mathematics, English, Science, Social Studies}. Cardinality: 4.
5. Set I: Prime numbers between 1 and 100. Elements: {2, 3, 5, 7, 11, ..., 97}. Cardinality: 25.
6. Set S: Distinct letters from the word 'araling panlipunan'. Elements: {a, r, l, i, n, g, p, u}.
7. Set F: Vowels from the word 'example'. Elements: {a, e}.
8. Set U: Consonants from the word 'english'. Elements: {n, g, l, s, h}.
9. Set N: Composite numbers from 11 to 20. Elements: {12, 14, 15, 16, 18, 20}. Cardinality: 6.