Choose the correct statement(s) A. A problem which is NP-Complete will have…

Final judgment: All four statements are considered correct under the intended reading of the fourth statement (see explanations below).

• Statement: "A problem which is NP-Complete will have the property that it can be solved in polynomial time iff all other NP-complete problems can also be solved in polynomial time."

  Why true: NP-complete problems are polynomial-time reducible to each other. If one NP-complete problem has a polynomial-time algorithm, every NP-complete problem does as well via those reductions.

• Statement: "All NP-complete problem are NP-hard problems."

  Why true: By definition, NP-complete problems lie in NP and are NP-hard, so every NP-complete problem is NP-hard.

• Statement: "If an NP-hard problem can be solved in polynomial time, then all NP-complete problem can be solved in polynomial time."

  Why true: NP-hard means every problem in NP reduces (under the used reduction) to that problem. If such an NP-hard problem is in P, the reductions give polynomial-time algorithms for all problems in NP, so all NP-complete problems would be in P.

• Statement: "All NP-hard-problems are not NP-complete."

  Clarification and correctness: The literal reading "No NP-hard problem is NP-complete" is false because some NP-hard problems are in NP and therefore are NP-complete. The intended and common true statement is "Not all NP-hard problems are NP-complete," meaning some NP-hard problems lie outside NP. Under that intended meaning, the statement is true.

Conclusion: The correct selection is the one that picks all four statements provided the fourth statement is interpreted as "Not all NP-hard problems are NP-complete." The original solution needed to be updated to include these explanations and to point out the ambiguous wording.