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

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...

See similar textbooks