If A and B are sets, several other sets can be constructed from them: the intersection of A and B, АПВ3 (x: хEA and x € B}; /| B N A = A N B. the union of A and B, AUB 3 (x: x Е A or x € B}; // BUA = A U B. and the set difference, A but not B, A\B {x: x € A and x ¢ B}. // Is B \ A = A \ B? // The set A \ B is sometimes called the "relative complement" of B in A. When A N B = Ø, sets A and B are said to be disjoint. /| A and B have no common element. The number of elements in a set S is called the cardinality of S and denoted by |S|. When this is a finite number, then |S| e N, and when |S = n, we’ll say that S is an n-set. For any pair of sets, |AUB| = |A|+|B| – |AN B|, and when A and B are disjoint, |AUB| = |A|+ |B|. // since AN B = Ø Furthermore, we always have |AUB| = |A \ B| +|B \ A| + |A N B|. Example 2.1.1: Operations, Sizes, and Subsets Suppose A is the set of odd integers less than 10 and B is the set of primes less than 10. Then = {2,3,5,7} A = {1,3,5,7,9} and ANB = {3,5,7} and AUB = {1,2,3,5,7,9} A \ B = {1,9} and B \ A = {2}; - |AN B| = 5+4 – 3 = |A \ B| + |B \ A| + |A N B| = 2+1+3. 6 = |AUB| = |A| + |B|

If A and B are sets, several other sets can be constructed from them: the intersection of A and B, АПВ3 (x: хEA and x € B}; /| B N A = A N B. the union of A and B, AUB 3 (x: x Е A or x € B}; // BUA = A U B. and the set difference, A but not B, A\B {x: x € A and x ¢ B}. // Is B \ A = A \ B? // The set A \ B is sometimes called the "relative complement" of B in A. When A N B = Ø, sets A and B are said to be disjoint. /| A and B have no common element. The number of elements in a set S is called the cardinality of S and denoted by |S|. When this is a finite number, then |S| e N, and when |S = n, we’ll say that S is an n-set. For any pair of sets, |AUB| = |A|+|B| – |AN B|, and when A and B are disjoint, |AUB| = |A|+ |B|. // since AN B = Ø Furthermore, we always have |AUB| = |A \ B| +|B \ A| + |A N B|. Example 2.1.1: Operations, Sizes, and Subsets Suppose A is the set of odd integers less than 10 and B is the set of primes less than 10. Then = {2,3,5,7} A = {1,3,5,7,9} and ANB = {3,5,7} and AUB = {1,2,3,5,7,9} A \ B = {1,9} and B \ A = {2}; - |AN B| = 5+4 – 3 = |A \ B| + |B \ A| + |A N B| = 2+1+3. 6 = |AUB| = |A| + |B|

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter17: Linked Lists

Section: Chapter Questions

Problem 5PE

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