Problems on sets: counting elements and comparing sets. Specifically, find n(N) for N = 11, 12, 13, 14, n(S) for S = 1, 4, 9, ..., 49, and determine if A = e, f, g, h equals B = g, f, h, e, and if X =

Here are the solutions to the set theory problems. 2. Let's say and write the correct answers in the blank spaces. a) Step 1: Identify the elements in set N. N = \11, 12, 13, 14\ Step 2: Count the number of elements in N. There are 4 elements in set N. n(N) = 4 b) Step 1: Identify the elements in set S. The set S = \1, 4, 9, , 49\ consists of perfect squares. The elements are 1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25, 6^2=36, 7^2=49. So, S = \1, 4, 9, 16, 25, 36, 49\. Step 2: Count the number of elements in S. There are 7 elements in set S. n(S) = 7 3. Let's say and write whether the following sets are equal or not. a) Step 1: Compare the elements of set A = \e, f, g, h\ and set B = \g, f, h, e\. Both sets contain exactly the same elements: e, f, g, h. The order of elements does not matter in a set. Step 2: Determine if the sets are equal. Since all elements are identical, sets A and B are equal. A and B are equal b) Step 1: Compare the elements of set X = \3, 6, 9, 12\ and set Y = \1, 3, 5, 7\. Set X contains elements 3, 6, 9, 12. Set Y contains elements 1, 3, 5, 7. Step 2: Determine if the sets are equal. The sets do not contain exactly the same elements (e.g., 6, 9, 12 are in X but not Y; 1, 5, 7 are in Y but not X). X and Y are not equal 4. Let's say and write whether the following sets are overlapping or disjoint. a) Step 1: Identify the elements in set P = \1, 3, 5, 7, 9\ and set Q = \2, 4, 6, 8\. Step 2: Check for common elements between P and Q. There are no elements that are present in both set P and set Q. Step 3: Determine if the sets are overlapping or disjoint. Since they have no common elements, P and Q are disjoint. P and Q are disjoint b) Step 1: Identify the elements in set A = \5, 10, 15, 20\ and set B = \4, 8, 12, 16, 20\. Step 2: Check for common elements between A and B. The element 20 is present in both set A and set B. Step 3: Determine if the sets are overlapping or disjoint. Since they have at least one common element (20), A and B are overlapping. A and B are overlapping Send me the next one 📸