Selected Exercises in Algebra by Rocco Chirivì & Ilaria Del Corso & Roberto Dvornicich

Author:Rocco Chirivì & Ilaria Del Corso & Roberto Dvornicich
Language: eng
Format: epub
ISBN: 9783030361563
Publisher: Springer International Publishing

(ii)We can choose the set Y = (A ∪ B) ∩ C in ways. Given an element of Y , it can belong to A ∖ B, B ∖ A or A ∩ B; consequently, we have 38 ways to distribute the elements of Y  among A and B.

By a similar argument, each element of X ∖ Y  can be assigned to any one of five sets: X ∖ (A ∪ B ∪ C), A ∖ (B ∪ C), B ∖ (A ∪ C), C ∖ (A ∪ B) or (A ∩ B) ∖ C. This gives 512 ways to place elements of X ∖ Y .

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