  In the paper we solve few problems proposed by Prapanpong Pongsriiam. Let
$f(n)$ denote the number of relatively prime subsets of $\{1, 2, 3, \dots, n\}$
and $g(n)$ denote the number of subsets $A$ of $\{1, 2, 3, \dots, n\}$ such
that gcd$(A)>1$ and gcd$(A, n+1)=1$ . We show that $f_n^2-f_{n-k}f_{n+k}>0$ for
$n\geq k+1\quad (k\geq2)$. We also show
$\frac{g(6n-2)}{g(6n-4)}>\frac{g(6n)}{g(6n-2)}>\frac{g(6n+2)}{g(6n)}<\frac{g(6n+4)}{g(6n+2)}$
for large $n$.
