1. 15.1 Inclusion/Exclusion OBJ:  to use the inclusion- exclusion principle to solve counting problems involving intersections and unions of sets

2. DEF:  The Inclusion-Exclusion Principle

3. EX:  How many positive integers less than 200 are divisible by 3 or 5?

4. EX:  Of the first 100 positive integers, 25 are prime, 9 are factors of 100, and 68 are neither prime or a factor of 100 How many are: a) both prime and a factor of 100? b) a factor of 100 but not prime?

5. EX:  Of the 540 seniors at Central High School, 335 are taking mathematics, 287 are taking science, and 220 are taking both mathematics and science. How many are taking neither mathematics nor science?

6. EX:  Of 150 students who are taking at least one science class, 45 are taking Biology, 75 are taking Chemistry, and 75 are taking Physics. Fifteen students are taking both Chemistry and Physics, 35 are taking only Chemistry, 25 are taking Biology and Chemistry, and no one is taking all three classes. How many students are taking only Biology?