Complement after set difference inside a fixed universe: Given U = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, A = {3, 5, 7, 9, 11}, and B = {7, 8, 9, 10, 11}. Compute (A − B)′ with respect to U.

Introduction / Context:Operations in order: compute set difference A − B, then take the complement relative to U. When answers include elements outside U or miss required ones, “None of these” can be correct if no listed set matches the true complement.

Given Data / Assumptions:

• U = {2,3,4,5,6,7,8,9,10,11}
• A = {3,5,7,9,11}
• B = {7,8,9,10,11}

Concept / Approach:First find A − B: keep elements in A that are not in B. Then complement the result in U by removing those from U.

Step-by-Step Solution:A − B = {3,5} (since 7,9,11 are in B)Complement in U: U \\ {3,5} = {2,4,6,7,8,9,10,11}

Verification / Alternative check:Scan options: (a) includes 12 (not in U) and wrongly includes 3 and 5; (b) includes 12 and misses 7,9; (c) misses 7 and includes 11 but not 7 incorrectly. None matches {2,4,6,7,8,9,10,11}.

Why Other Options Are Wrong:They either step outside U or omit/include wrong elements relative to the computed complement.

Common Pitfalls:Forgetting to ground complements in the specified universe and allowing stray elements like 12 to appear.

Final Answer:None of these