How can the cardinality of set A be determined through the provided statements regarding its subsets?

The correct answer highlights the relationship between the cardinality of a set and its subsets, particularly focusing on subsets of specific cardinalities. In set theory, the cardinality of a set refers to the number of elements contained within that set.

When considering subsets of specific sizes, such as those with cardinalities of 2 and 3, one can utilize combinatorial methods to derive the total number of subsets. Specifically, the number of ways to choose subsets of size k from a set of size n is given by the binomial coefficient, represented as "n choose k" or C(n, k).

Using this combinatorial approach allows for direct connections between subsets of various sizes and the total cardinality of the set. For example, knowing the number of subsets of size 2 and size 3 can provide insights into the total number of elements when analyzed together, since these values can help reconstruct the original set size through established relationships in combination theory.

This insight is particularly useful as it ties together two key cardinalities to derive the complete picture of the set, whereas other methods may not provide as direct or effective a means to ascertain the overall cardinality. Therefore, analyzing the relationships between subsets of different sizes is a powerful tool in determining the cardinal