Thanks for your patience with our reply. Here's some hints:

- 3.9: For problems like this, try to do the opposite. Try to build a set for as long as possible so that any two numbers chosen are relatively prime. For example, 1 is good to include, as it is relatively prime with everything. Hint: Primes are probably also good to try to include.

- 3.10: By Bezout's Identity, we can replace gcd(m,n) by a*m + b*n for integers a and b. Try to rewrite the expression from here. Hint: We know that $\displaystyle \binom{A}{B}$ is always an integer for any non-negative integers $A$ and $B$, can you take advantage of this?

Hope this helps!

General Note: We do highly recommend students get the textbooks for the live classes. The textbooks do include the solution ideas for all the Example Problems, numbered 1 through 10 of each chapter.