Question: how to answer Let A, B, and C be sets, and let X = A U B. (a) Write [X n C| in terms of

how to answer

how to answer Let A, B, and C be sets, and let X
Let A, B, and C be sets, and let X = A U B. (a) Write [X n C| in terms of |An CI, IB n CI, and |An Bn CI. Hint: In the following Venn diagram, XN C is the shaded area. A B C O |AnCI + IBN CI + |AnBnCI O |AnBACI - LANCI + IBn CI O AnCI - AnBACI + IBn CI - AnBACI O LANCI + IBN CI - AnBnCI O |AnBACI + |AnCI - IBn CI (b) Write [A U B U C| in terms of A, B, C, |An BI, |An CI, IBN CI, and |An Bn CI. (The result is the inclusion-exclusion principle for three sets.) O IA| + 18| + |CI - |AnBn CI O JAI + IBI + ICI - |AnBI - |An CI - IBn CI - |AnBn CI O IAI + IBI + ICI - |AnBI - |An CI - IBN CI O |AI + IB| + [CI - |AnBI - |An CI - IBN CI + |AnBn CI O |An BI + |AnCI + 1Bn CI - |AI - IBI - ICI + |AnBn CI

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