Given a set of non-negative integers, and a value S, determine if there is a subset of the given set with sum equal to S.

This problem can be solved using a method called dynamic programming. Here are the steps:

1. Initialize a boolean 2D array dp[n+1][sum+1], where n is the size of the given set. The value of dp[i][j] will be true if there is a subset of the set with sum equal to j.

2. Set dp[i][0] = true for all i, because there is always an empty subset with sum 0.

3. Set dp[0][i] = false for all positive i, because there is no subset with positive sum when the set is empty.

4. For each element in the set, iterate from 1 to n (i.e., for i=1 to n). For each possible sum from 0 to sum (i.e., for j=0 to sum), set dp[i][j] = dp[i-1][j] if dp[i-1][j] equals true or if the current element is less than or equal to the current sum and dp[i-1][j-element] equals true.

5. Finally, return dp[n][sum]. If it is true, then there is a subset with sum equal to S. Otherwise, there is no such subset.