The number of seniors majoring in history using the inclusion-exclusion principle is 456.
Finding the number of elements in the union of two finite sets can be done using the principle of inclusion and exclusion.
There are 523 seniors of history majors or math majors or both in a university.
There are 33 seniors majoring in both history and math and 100 senior math majors.
Let A and B be the sets of math majors and history majors, respectively. Then by the inclusion-exclusion principle:
| A ∪ B | = | A | + | B | − | A ∩ B |
The number of history majors is:
| A | = | A ∪ B | + | A ∩ B | − | B |
| A | = 523 + 33 − 100
| A | = 456
The number of seniors majoring in history using the inclusion-exclusion principle is 456.
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