Statement (a) is false because running time also depends on the time required to solve each subproblem, not only the number of subproblems.

Statement (b) is true because cyclic dependency creates a circular dependency, so the recurrence cannot be used directly in a correct dynamic program.

Statement (c) is false because bottom-up DP and memoized recursion usually have the same asymptotic time complexity.

Statement (d) is false because if $X$ is reduced to an NP-hard problem, it does not prove that $X$ is NP-hard. To prove $X$ is NP-hard, a known NP-hard problem should be reduced to $X$.

So, only statement (b) is true.