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 $7?$