Recovering |B| from |A|, |A ∪ B|, and |A ∩ B|: If set A has 40 elements, |A ∪ B| = 60 elements, and |A ∩ B| = 10 elements, how many elements does set B have?

Introduction / Context:This uses inclusion-exclusion solved for |B|. The original stem had a symbol typo; we apply the standard interpretation |A ∩ B| = 10 via Recovery-First to make it solvable.

Given Data / Assumptions:

• |A| = 40
• |A ∪ B| = 60
• |A ∩ B| = 10 (repaired)

Concept / Approach:|A ∪ B| = |A| + |B| − |A ∩ B| → solve for |B|.

Step-by-Step Solution:60 = 40 + |B| − 10|B| = 60 − 30 = 30

Verification / Alternative check:Check: 40 + 30 − 10 = 60 (consistent).

Why Other Options Are Wrong:40, 45, 50 contradict the union size when back-substituted.

Common Pitfalls:Reading the misprinted symbol literally without applying standard set identity.

Final Answer:30