Let's break down the questions and provide solutions based on the images you uploaded:

Image 1:

A. Identify the premise and conclusion in each of the following arguments.

1. First Argument:

   • Premise: The building of the College of Informatics and Computing Sciences, College of Engineering, Architecture and Fine Arts, and the College of Industrial Technology in BatStateU Alangilan are made out of cement.
   • Conclusion: Therefore, all buildings of Batangas State University are made out of cement.
   • This is an example of deductive reasoning because the argument starts with specific premises and draws a general conclusion.

2. Second Argument:

   • Premise: All birds have wings. Eagle is a bird.
   • Conclusion: Therefore, eagle is a bird.
   • This argument also uses deductive reasoning. It starts with a general statement and concludes a specific case.

B. Use inductive reasoning to predict the next three numbers on the following series of numbers.

1. Series a: 3, 7, 11, 15, 19, 23, __, __, __

   • The difference between consecutive numbers is 4.
   • Next numbers: 27, 31, 35.

2. Series b: 1, 2, 6, 15, 31, __, __, __

   • The difference between consecutive numbers increases as follows: +1, +4, +9, +16. The next differences will be +25, +36, +49.
   • Next numbers: 56, 92, 141.

3. Series c: 1, 4, 9, 16, 25, 36, 49, __, __, __

   • These numbers are squares of consecutive integers (1², 2², 3², etc.).
   • Next numbers: 64, 81, 100.

Image 2:

1. Complete the next possible equation in the following series:

• Given pattern:
  • 37 × 3 = 111
  • 37 × 6 = 222
  • 37 × 9 = 333
  • 37 × 12 = 444
• This pattern suggests that the multiplier increases by 3 each time. The next multiplier should be 15.
• Therefore, the next equation is:
  37 × 15 = 555.

2. Formula for the sequence of square tiles:

• You are asked to find a formula for the number of square tiles in the sequence shown by $a_1, a_2, a_3, a_4$.
• The number of tiles follows a visible increasing pattern.
• To find the exact formula, observe how the number of tiles increases with each step. We would need to break down the visual structure of each figure, which may require further analysis of the shapes in the sequence.

Let me know if you'd like further details on this!

Questions for further practice:

1. How would you define the difference between inductive and deductive reasoning?
2. Can you create a similar sequence that uses a different rule for the gaps between numbers?
3. How can the formula for the number of tiles be generalized for an arbitrary term $n$?
4. What assumptions are made in deductive reasoning and how can they lead to invalid conclusions?
5. What are some real-life scenarios where inductive reasoning is commonly used?

Tip: When analyzing number sequences, always start by checking for a pattern in differences or ratios between consecutive terms.