Final answer:
To determine the equivalence of sets, both the number of elements and a matching transformation must be considered. All provided sets have four elements but differ in the nature of these elements, and there are no transformations to match one set with another. Hence, sets A, B, C, and D are not equivalent.
Step-by-step explanation:
To determine which of the following sets are equivalent, we need to compare the number of elements in each set and then see if there is a one-to-one correspondence between any of the sets. The sets given are:
- Set A: {1, 2, 3, 4}
- Set B: {2, 4, 6, 8}
- Set C: {3, 6, 9, 12}
- Set D: {4, 8, 12, 16}
Each set has four elements, so they all have the same cardinality. However, for sets to be equivalent, the elements need to match one another through a function or transformation that can be applied consistently across all elements. Looking at the sets, there is no clear transformation that makes them equivalent. Set A contains consecutive natural numbers, set B is comprised of even numbers with a common factor of 2, set C has multiples of 3, and set D is made up of multiples of 4. Since there isn't any set with the exact same elements or an applicable transformation function, none of these sets are equivalent.