Using the universal set U = 1, 2, ..., 12, let E be the set of even numbers and M be the set of multiples of 3. Find n(M), E ∩ M, and a possible value for y if y ∈ (E ∪ M).

You're on a roll — Here are the solutions for the questions. Question 1: Set Theory First, let's define the sets based on the given information: The universal set E consists of integers x such that 1 x 12. E = \1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\ Set E consists of even numbers within E. E = \2, 4, 6, 8, 10, 12\ Set M consists of multiples of 3 within E. M = \3, 6, 9, 12\ a) Find n(M). Step 1: Count the number of elements in set M. M = \3, 6, 9, 12\ has 4 elements. The answer is n(M) = 4. b) Write down the set E M. Step 1: Identify the elements that are common to both set E and set M. E = \2, 4, 6, 8, 10, 12\ M = \3, 6, 9, 12\ The common elements are 6 and 12. The answer is E M = \6, 12\. c) y (E M). Write down a possible value of y. Step 1: Find the union of set E and set M, which includes all elements in E or M (or both). E M = \2, 3, 4, 6, 8, 9, 10, 12\ Step 2: Choose any element from the set E M. For example, 2. A possible value of y is 2. (Other valid answers include 3, 4, 6, 8, 9, 10, 12).