Two players A and B play the following game:
Start with the set S of the first 25 natural numbers: S={1,2,…,25}.
Player A first picks an even number x₀ and removes it from S:
We have S:=S−x₀.
Then they take turns (starting with B) picking a number x_n∈S which is either divisible by x_n-1 or divides x_n-1 and removing it from S.

The player who can not find a number in S which is a multiple of the previous number or is divisible by it loses.

Which player has the winning strategy and what is it?

Source: someone sent it by Email.