To use the inclusion/exclusion principle to obtain |A U B|, we need |A|, |B| and |A ∩ B|.A ∩ B = The set of all integers that are both multiples of 3 and 5, which also is the set of integers that are multiples of 15.A U B = The set of all integers from 1 to 1000 that are multiples of either 3 or 5.Let us assume that B = set of all integers from 1 to 1000 that are multiples of 5.Let us assume that A = set of all integers from 1 to 1000 that are multiples of 3.Example 1: How many integers from 1 to 1000 are either multiples of 3 or multiples of 5?.Hence, we have |B| = 14.) and the multiple of 21… n(A ∩ B) = 4Įxample: Inclusion and Exclusion Principle Similarly for multiples of 7, each multiple of 7 is of the form 7q for some integer q from 1 through 14.From 1 to 100, every third integer is a multiple of 3, each of this multiple can be represented as 3p, for any integer p from 1 through 33, Hence |A| = 33.= 33 + 14 – 4 = 43 (by counting the elements.First note that A ∩ B is the set of integers from 1 through 100 which are multiples of 21.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |