Question

For an integer n ≥ 1, consider the set {1, 2, ..., n}. Define the weight of a subset A to be the integer...

a) Sum of elements in A
b) Product of elements in A
c) Largest element in A
d) Smallest element in A

Answer 1

The weight of a subset A of the set {1, 2, ..., n} can be defined by the sum of its elements, the product of its elements, the largest element, or the smallest element in the subset.

Step-by-step explanation:

The question asks to define the weight of a subset A of the set {1, 2, ..., n} for an integer n ≥ 1. The weight of subset A can be defined in several ways: The sum of elements in subset A, which is the total of all the numbers included in the subset.

The product of elements in subset A, which is the multiplication of all numbers included in the subset. The largest element in subset A, which is the highest number within the subset. The smallest element in subset A, which is the lowest number within the subset.

For example, if n is 5 and A is {2, 4}, the sum would be 6, the product would be 8, the largest element would be 4, and the smallest would be 2. Defining the weight can depend on the context of the problem or the specific criteria you are looking at.