B. Classify each set as either finite (F) or infinite (I) by encircling the correct answer and give its
cardinality.
F I n(A) = __________ 1. A = set of odd prime numbers
F I n(A) = __________ 2. A = {factors of 12}
F I n(A) = __________ 3. A = {counting numbers between 1 and 2}
F I n(A) = __________ 4. A = {x/x is a counting number and x + 3 = 4}
F I n(A) = __________ 5. A = set of letters in the word ‘PHILIPPINES’
F I n(A) = __________ 6. A = set of letters in the word ‘INFINITE’
F I n(A) = __________ 7. A = set of PSHS campuses
F I n(A) = __________ 8. A = {core values of Pisay}
F I n(A) = __________ 9. A = set of natural numbers greater than 1 but less than 5
F I n(A) = __________ 10. A = {5, 10, 15, 20, 25, ...}

Let's go through each set and classify them as finite (F) or infinite (I) and determine their cardinality (the number of elements).

1. **A = set of odd prime numbers**  
   - **Classification**: Infinite (I)  
   - **Cardinality**: Infinite  
     There are infinitely many prime numbers, and the odd ones (e.g., 3, 5, 7, 11, etc.) form an infinite set.

2. **A = {factors of 12}**  
   - **Classification**: Finite (F)  
   - **Cardinality**: 6  
     The factors of 12 are {1, 2, 3, 4, 6, 12}, so the set has 6 elements.

3. **A = {counting numbers between 1 and 2}**  
   - **Classification**: Finite (F)  
   - **Cardinality**: 0  
     There are no counting numbers strictly between 1 and 2, so the set is empty, and the cardinality is 0.

4. **A = {x | x is a counting number and x + 3 = 4}**  
   - **Classification**: Finite (F)  
   - **Cardinality**: 1  
     Solving the equation \(x + 3 = 4\) gives \(x = 1\), so the set contains only one element, {1}.

5. **A = set of letters in the word ‘PHILIPPINES’**  
   - **Classification**: Finite (F)  
   - **Cardinality**: 7  
     The distinct letters in "PHILIPPINES" are {P, H, I, L, N, E, S}, which gives 7 unique elements.

6. **A = set of letters in the word ‘INFINITE’**  
   - **Classification**: Finite (F)  
   - **Cardinality**: 5  
     The distinct letters in "INFINITE" are {I, N, F, T, E}, which gives 5 unique elements.

7. **A = set of PSHS campuses**  
   - **Classification**: Finite (F)  
   - **Cardinality**: 16  
     As of the latest information, there are 16 Philippine Science High School (PSHS) campuses.

8. **A = {core values of Pisay}**  
   - **Classification**: Finite (F)  
   - **Cardinality**: 4  
     The core values of PSHS are typically Integrity, Excellence, Service, and Resilience, so the set has 4 elements.

9. **A = set of natural numbers greater than 1 but less than 5**  
   - **Classification**: Finite (F)  
   - **Cardinality**: 3  
     The natural numbers between 1 and 5 are {2, 3, 4}, so the set has 3 elements.

10. **A = {5, 10, 15, 20, 25, ...}**  
    - **Classification**: Infinite (I)  
    - **Cardinality**: Infinite  
      This is the set of multiples of 5, and it is an infinite sequence.

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Let me know if you want any additional details or explanations. Here are some follow-up questions:

1. What is the cardinality of the set of even prime numbers?
2. Can you give an example of a finite set with a cardinality of 10?
3. Is the set of real numbers between 0 and 1 finite or infinite?
4. What is the difference between finite and infinite sets?
5. How do you find the cardinality of a set with repeating elements like in words?

**Tip**: When dealing with finite sets, the cardinality is simply the number of unique elements in the set.

B. Classify each set as either finite (F) or infinite (I) by encircling the correct answer and give its cardinality.
F I n(A) = __________ 1. A = set of odd prime numbers
F I n(A) = __________ 2. A = {factors of 12}
F I n(A) = __________ 3. A = {counting numbers between 1 and 2}
F I n(A) = __________ 4. A = {x/x is a counting number and x + 3 = 4}
F I n(A) = __________ 5. A = set of letters in the word ‘PHILIPPINES’
F I n(A) = __________ 6. A = set of letters in the word ‘INFINITE’
F I n(A) = __________ 7. A = set of PSHS campuses
F I n(A) = __________ 8. A = {core values of Pisay}
F I n(A) = __________ 9. A = set of natural numbers greater than 1 but less than 5
F I n(A) = __________ 10. A = {5, 10, 15, 20, 25, ...}

Learn how to classify sets as finite or infinite and determine their cardinality through examples like prime numbers, factors of 12, and the letters in words. Suitable for Grades 7-9 students exploring set theory and cardinality.

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