Chapter 8, Problem 10RQ

a) Give a formula for the number of elements in the union of three sets.

b) Explain why this formula is valid.

c) Explain how to use the formula from (a) to find the number of integers not exceeding 1000 that are divisible by 6, 10, or 15. d) Explain how to use the formula from (a) to find the number of solutions in nonnegative integers to the equation $x_1+x_2+x_3+x_4=22$ with $x_1<8,x_2<6$ , and $x_3<5$ .