Final answer:
The cardinality of the set (B-A) ∪ C is 5, because when we calculate B-A, we get {4,5}, and unionizing this with C results in {1,3,4,5,7}, which has 5 unique elements.
Step-by-step explanation:
The question asks for the cardinality of the set (B-A) ∪ C, where set A = {1,2,3}, set B = {2,3,4,5}, and set C = {1,3,5,7}. The difference of sets B and A, denoted as (B-A), means we remove any elements from set B that are also in set A. Thus, B-A = {4,5} since 2 and 3 are removed.
The union of sets (B-A) and C, denoted as (B-A) ∪ C, combines the unique elements of both sets, resulting in {4,5} ∪ {1,3,5,7} which simplifies to {1,3,4,5,7}. The cardinality of the set is the number of elements in the set, so the answer to the question is 5, since there are 5 elements in {1,3,4,5,7}.