Cardinalities with inclusion–exclusion (Recovery-First applied): If n(A) = 40, n(B) = 26 and n(A ∩ B) = 16, compute n(A ∪ B).

Introduction / Context:The original stem repeated n(A ∩ B) on both sides, which is likely a typographical slip. Using Recovery-First, we repair the question to find n(A ∪ B) from n(A), n(B), and n(A ∩ B).

Given Data / Assumptions:

• n(A) = 40
• n(B) = 26
• n(A ∩ B) = 16

Concept / Approach:For any two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Subtracting the overlap prevents double counting shared elements.

Step-by-Step Solution:n(A ∪ B) = 40 + 26 − 16= 66 − 16 = 50

Verification / Alternative check:If A and B were disjoint (n(A ∩ B) = 0), we would have 40 + 26 = 66; an overlap of 16 reduces the union size to 50, consistent with the formula.

Why Other Options Are Wrong:30 and 40 undercount; 60 ignores the overlap; 42 is arbitrary and not obtained by the correct formula.

Common Pitfalls:Adding the two sizes without subtracting the intersection or misreading the repaired stem; always check for overlaps to avoid double counting.

Final Answer:50