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Given two sets A and B with n(A) = 1000 and n(B) = 500, and with n(A ∩ B) at least 1, let n(A ∪ B) = p. Which range must p satisfy?

1. 500 ≤ p ≤ 1000
2. 1001 ≤ p ≤ 1498
3. 1000 ≤ p ≤ 1498
4. 1000 ≤ p ≤ 1499

Correct answer: 1000 ≤ p ≤ 1499

Solution

n(AuB) = 1000 + 500 - n(AnB). Since n(AnB) can be from 1 (max union) up to 500 (min union, B subset of A), p ranges from 1000 to 1499, i.e. 1000 <= p <= 1499.

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