Solved: For each of exercises below, the number of
Chapter 9, Problem 39E(choose chapter or problem)
Problem 39E
For each of exercises below, the number of elements in a certain set can be found by computing the number in some larger universe that are not in the set and subtracting this from the total. In each case, as indicated by exercise, De Morgan’s laws and the inclusion/exclusion rule can be used to compute the number that are not in the set.
Exercise
Fill in the reasons for each step below. If A and B are sets in a finite universe U, then
Exercise
For each of exercises below, the number of elements in a certain set can be found by computing the number in some larger universe that are not in the set and subtracting this from the total. In each case, as indicated by exercise, De Morgan’s laws and the inclusion/exclusion rule can be used to compute the number that are not in the set.
How many integers from 1 through 999,999 contain each of the digits 1, 2, and 3 at least once? (Hint: For each i = 1, 2, and 3, let Ai be the set of all integers from 1 through 999,999 that do not contain the digit i.)
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