Intersection of two prime-heavy sets — compute A ∩ B explicitly: Given A = {2, 3, 5, 7, 11} and B = {1, 3, 5, 7, 9, 11}, determine A ∩ B.
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A{ 2, 3, 5, 7, 11 }
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B{ 1, 3, 5, 7, 9, 11 }
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C{ 3, 5, 7, 11 }
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D{ 2, 3, 5, 7, 9, 11 }
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E{ 1, 2, 3, 5, 7, 9, 11 }
Answer
Correct Answer: { 3, 5, 7, 11 }
Explanation
Introduction / Context:Set intersection retains only elements common to both sets. Here A is a prime list up to 11, while B mixes odds with the prime 11; we simply keep shared elements.
Given Data / Assumptions:
- A = {2, 3, 5, 7, 11}
- B = {1, 3, 5, 7, 9, 11}
Concept / Approach:A ∩ B = {x : x ∈ A and x ∈ B}. Check each member of A against B to keep the common ones.
Step-by-Step Solution:2 ∈ A but 2 ∉ B → exclude3, 5, 7, 11 appear in both → includeIntersection = {3, 5, 7, 11}
Verification / Alternative check:Scan B: {1, 3, 5, 7, 9, 11} → removing 1 and 9 (not in A) leaves {3, 5, 7, 11}.
Why Other Options Are Wrong:Option A equals A (not intersection); option B equals B; option D and option E introduce elements not present in both sets (2 or 1, 9).
Common Pitfalls:Confusing union and intersection; forgetting that duplicates do not matter in set notation.
Final Answer:{ 3, 5, 7, 11 }