Let the set A= {1,2,3,4,5,6,7,8,9}. Find the minimum number of integers n ∈ Z, selected from the set A, such that the sum of their integers is even.

To find the minimum number of integers n ∈ Z (integers) selected from the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} such that the sum of their integers is even, we need to consider the properties of even and odd numbers. An even number can be represented as 2k, where k is an integer. An odd number can be represented as 2k + 1. Let's consider the numbers in set A: Even numbers in A: {2, 4, 6, 8} Odd numbers in A: {1, 3, 5, 7, 9} Now, let's look at some possible combinations to achieve an even sum: If we select any two even numbers, their sum will be even (e.g., 2 + 4 = 6). If we select any two odd numbers, their sum will be even (e.g., 1 + 3 = 4). If we select one even number and one odd number, their sum will be odd (e.g., 2 + 1 = 3). So, to achieve an even sum, we need to select either: Two even numbers (2 numbers) or Two odd numbers (2 numbers). In both cases, we need to select a minimum of 2 integers from set A to guarantee an even sum. Therefore, the minimum number of integers n ∈ Z that must be selected is 2.