Question

A student says that every time she adds one element to a finite set, she doubles the number of subsets. Is she correct? Explain and illustrate with an example.

Answer 1

No, the student is not correct. Adding one element to a finite set does not double the number of subsets. For example, if we start with a set of three elements, there are eight subsets. When we add one more element, the number of subsets increases to 16, not double the original amount. The number of subsets in a set with n elements is determined by 2^n, not by doubling.