Consider $n$ symbols and every elements of $P_m(X)$ as a number in base $n$. Write every element of $P_m(X)$ in "Lexographical order" (increasing or decreasing) and arrange these elements in this Lexographical order also in set $P'_m(X)$. This new set $P'$ satisfied both condition: $(A)$ is obvious and for $(B)$, notice any two consecutive element of $P'$, there is no other number of $P$ between these two element so the digits of them differ by only one digit, so satisfy. As for example, $n=5$, $m=3$, $X=\{ 1, 2, 3, 4, 5 \}$ and $P_3(X)$ in some random order (commas are discarded), \[ P_3(X)=\{ 123, 145 , 345 , 125 , 234 , 134 , 235 , 135 , 245 , 124 \} \]In the above set, each element is arranged in increasing order but the set itself is not. Below is the arrangement of $P_3(X)$ itself in increasing order: \[ P'_3(X)= \{ 123,124,125,134,135,145,234,235,245,345 \} \]