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At a certain university 523 of the seniors are history majors or math majors (or both). There are 100 senior math majors, and 33 seniors are majoring in both history and math. How many seniors are majoring in history? Let A be the set of seniors who are math majors and let B be the set of seniors who are history majors. Then AUB is the set of seniors who are history majors or math majors or both, and AnB is the set of seniors who are majoring in both history and math. By the inclusion exclusion principle we have |AU B| = |A|+|B| − |AnB| and thus we have 523 100+ |B|-33 so the number of seniors majoring in history is |B| = 523 - 100 +33 = 556. How many 4-digit positive integers are there that are even or contain no 0's?

At a certain university 523 of the seniors are history majors or math majors (or both). There are 100 senior math majors, and 33 seniors are majoring in both history and math. How many seniors are majoring in history? Let A be the set of seniors who are math majors and let B be the set of seniors who are history majors. Then AUB is the set of seniors who are history majors or math majors or both, and AnB is the set of seniors who are majoring in both history and math. By the inclusion exclusion principle we have |AU B| = |A|+|B| − |AnB| and thus we have 523 100+ |B|-33 so the number of seniors majoring in history is |B| = 523 - 100 +33 = 556. How many 4-digit positive integers are there that are even or contain no 0's?

Advanced Engineering Mathematics
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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At a certain university 523 of the seniors are history majors or math majors (or both). There are 100 senior math majors, and 33 seniors are majoring in both history and math. How many seniors are majoring in history? Let A be the set of seniors who are math majors and let B be the set of seniors who are history majors. Then AUB is the set of seniors who are history majors or math majors or both, and AnB is the set of seniors who are majoring in both history and math. By the inclusion exclusion principle we have |AUB| = |A|+|B|-|An B| and thus we have 100+ |B|-33 523 = so the number of seniors majoring in history is |B| = 523 – 100+ 33 = 556. How many 4-digit positive integers are there that are even or contain no 0's?
Transcribed Image Text:At a certain university 523 of the seniors are history majors or math majors (or both). There are 100 senior math majors, and 33 seniors are majoring in both history and math. How many seniors are majoring in history? Let A be the set of seniors who are math majors and let B be the set of seniors who are history majors. Then AUB is the set of seniors who are history majors or math majors or both, and AnB is the set of seniors who are majoring in both history and math. By the inclusion exclusion principle we have |AUB| = |A|+|B|-|An B| and thus we have 100+ |B|-33 523 = so the number of seniors majoring in history is |B| = 523 – 100+ 33 = 556. How many 4-digit positive integers are there that are even or contain no 0's?
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