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# Principle of Inclusion and Exclusion

Count to 100. How many of those numbers are odd or multiples of 5? Since 50 are odd and 20 are multiples of 5, at first glance the answer is 70...

70% of students passed the Mathematics examination, and

60% of students passes the Science examination.

What is the minimum percentage of students that passed **both** examinations?

How many numbers in the set \(\{1,2,\ldots,100\}\) are divisible by \(5\) or \(7?\)

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