Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Question
Let A, B, and C be sets, and let X = AU B. (a) Write Ix n c in terms of IAN CI, IBN C, and AnBn Cl. Hint: In the following Venn diagram, XnC is the shaded area. A B O IAN BNC| + |ANCI - IBN cl O ANC + IBN C| - |AN BNCI O JAN BNCIAN CI+ IBn Cl O JANCI + IBN CI + JAN BNCI O LANCI - IAN BNC + BNC - JAN BN cl (b) Write |A U BU CI in terms of A, B, C, IAN BI, JAN CI, IBC, and AnBnC). (The result is the inclusion-exclusion principle for three sets.) O AI + |B| + |C| - |AN BNCI O A + B + |C| - |AN B|- |ANCI - IB n cl O A + B + ICI- JAN BI - JANCI - IBN C + AnBn Cl O AI + |B| + |C| - |AN B|- |ANCI - IBN C| - |An Bn CI O JAN BI + IANC + IBN C| - |A| - |B| = |C| + |AnBn Cl
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Transcribed Image Text:Let A, B, and C be sets, and let X = AU B. (a) Write Ix n c in terms of IAN CI, IBN C, and AnBn Cl. Hint: In the following Venn diagram, XnC is the shaded area. A B O IAN BNC| + |ANCI - IBN cl O ANC + IBN C| - |AN BNCI O JAN BNCIAN CI+ IBn Cl O JANCI + IBN CI + JAN BNCI O LANCI - IAN BNC + BNC - JAN BN cl (b) Write |A U BU CI in terms of A, B, C, IAN BI, JAN CI, IBC, and AnBnC). (The result is the inclusion-exclusion principle for three sets.) O AI + |B| + |C| - |AN BNCI O A + B + |C| - |AN B|- |ANCI - IB n cl O A + B + ICI- JAN BI - JANCI - IBN C + AnBn Cl O AI + |B| + |C| - |AN B|- |ANCI - IBN C| - |An Bn CI O JAN BI + IANC + IBN C| - |A| - |B| = |C| + |AnBn Cl
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