Discrete Mathematics
# Principle of Inclusion and Exclusion

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?

In a class of students, \(64\text{%}\) of the students passed the physics exam and \(68\text{%}\) of the students passed the math exam.

What is the minimum percentage of students in the class that passed both exams?

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

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