Let A, B, and C be the sets such that AUB=AUC and AintersectionB=AintersectionC.
Show that B = C
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We know that XUY = X + Y + XintY
Here,
AUB = A + B + AintB.
AUC = A + C + AintC
But AUB = AUC
so, A + B + AintB = A + C + AintC
But A = A and AintB = AintC, these can be removed from both sides giving us,
B = C
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