Final answer:
The problem involves set theory, specifically calculating the total number of elements when sets are disjoint or have overlaps. Scenario (a) is a straightforward sum, while scenario (b) requires the principle of inclusion-exclusion.
Step-by-step explanation:
The question pertains to finding the number of elements in given sets with different conditions: when sets are pairwise disjoint and when there is a degree of overlap between the sets. For the case where sets are pairwise disjoint (a), the total number of elements is simply the sum of elements in each set since none are repeated across sets. However, in the second scenario (b), we have to consider the common elements between the pairs of sets and the elements common to all three sets to avoid counting them multiple times.
In the disjoint scenario, we add the given numbers together. For the scenario with overlaps, we use the principle of inclusion-exclusion, subtracting the number of common elements between each pair of sets and adding back those common to all three, ensuring we don't count these multiple times.