Compute (A ∩ U) ∩ (B ∪ C) in a finite universe: Given U = {2,3,4,5,6,7,8,9,10,11}, A = {2,4,7}, B = {3,5,7,9,11}, C = {7,8,9,10,11}, evaluate (A ∩ U) ∩ (B ∪ C).

Introduction / Context:Intersecting with U leaves A unchanged since A ⊆ U. Then intersect A with the union B ∪ C by simple element checks.

Given Data / Assumptions:

• A = {2,4,7}
• B = {3,5,7,9,11}
• C = {7,8,9,10,11}

Concept / Approach:Compute B ∪ C, then intersect with A.

Step-by-Step Solution:A ∩ U = AB ∪ C = {3,5,7,8,9,10,11}A ∩ (B ∪ C) = {2,4,7} ∩ {3,5,7,8,9,10,11} = {7}

Verification / Alternative check:Only 7 lies in all three relevant sets; 2 and 4 are not in B ∪ C.

Why Other Options Are Wrong:{9}, {6}, {5} are not in A; the multi-element set adds extras not present in A.

Common Pitfalls:Forgetting to take union before intersection; mixing elements not in A when intersecting.

Final Answer:{7}