State (without proof) the inclusion-exclusion formula for the cardinality of the union of two finite sets. Suppose that X, Y and Z are subsets of {1,2,3,..., 10} and |X| = |Y| = |Z| = 7. (i) Prove that |XnY| > 4. (ii) Deduce that XNYNZ is non-empty. [Hint: Consider (XnY)UZ.] State (without proof) the inclusion-exclusion formula for the cardinality of the union of three finite sets. Suppose that |A| = |B| = |C| = 6 and |ANB| = |ANC| = |BnC| = 2. Determine the smallest that |AUBUC| can be under these conditions. Give an example of three sets which achieve this. %3D

State (without proof) the inclusion-exclusion formula for the cardinality of the union of two finite sets. Suppose that X, Y and Z are subsets of {1,2,3,..., 10} and |X| = |Y| = |Z| = 7. (i) Prove that |XnY| > 4. (ii) Deduce that XNYNZ is non-empty. [Hint: Consider (XnY)UZ.] State (without proof) the inclusion-exclusion formula for the cardinality of the union of three finite sets. Suppose that |A| = |B| = |C| = 6 and |ANB| = |ANC| = |BnC| = 2. Determine the smallest that |AUBUC| can be under these conditions. Give an example of three sets which achieve this. %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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