In a department of 100 aerospace researchers, 65 have experience with CFD solvers, 45 have experience with structural FEA solvers, and 20 have experience with both CFD and FEA solvers. How many researchers in the department have experience with **neither** CFD nor FEA?

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### 1. Strategy & Theoretical Principles By the Principle of Inclusion-Exclusion for two sets $A$ (CFD) and $B$ (FEA): $$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$ The number of individuals belonging to neither set is: $$n((A \cup B)') = n(U) - n(A \cup B)$$ ### 2. Analytical Formulation & Calculation Given: - Total researchers $n(U) = 100$ - $n(A) = 65$ - $n(B) = 45$ - $n(A \cap B) = 20$ $$n(A \cup B) = 65 + 45 - 20 = 110 - 20 = 90$$ Number of researchers with neither experience: $$n((A \cup B)') = 100 - 90 = 10$$ ### 3. Distractor Forensics - Forgetting to subtract intersection: $65+45 = 110 > 100$, leading to confusion. - Subtracting 20 twice yields incorrect values. ### 4. Exam Trap & Standard Reference - **Trap Alert:** Always subtract the overlapping intersection $n(A \cap B)$ once. - **Standard Reference:** GATE General Aptitude Official Syllabus.

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