In "Araby," the narrator's idealization of Mangan's sister contrasts with the disappointing reality of the bazaar, highlighting the ironic gap between his romantic dreams and the bleakness of his surroundings. In "A&P," Sammy quits his job to defend the girls' honor, expecting them to appreciate his gesture, but they leave without acknowledging him, showing the ironic discrepancy between his heroic expectations and the indifferent reality of the situation.
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The short answer is that if you don't do so, the intersection is double counted. The longer answer follows: Suppose you have two events A and B which overlap. Then, Event A = (only A happens) and (both A and B happen). These two are mutually exclusive so that P(A) = P(A only) + P(both). Similarly, P(B) = P(B only) + P(both). Now, the event that A or B happen is the event that only A happens or only B happens or both happen. That is, P(A or B) = P(A only) + P(both) + P(B only) Adding and subtracting P(both) gives P(A or B) = P(A only) + P(both) + P(B only) + P(both) - P(both) Now, the first two are P(A) and the next two are P(B) So P(A or B) = P(A) + P(B) - P(both).
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