Assume that X and Y are two decision problems. Which of the following are true?

Check all that apply.

Select one or more:

a. If there is a polynomial-time reduction from X to Y, and a polynomial-time algorithm for X, then there is a

polynomial-time algorithm for Y

b. If there is a polynomial-time reduction from X to Y, and a polynomial-time algorithm for Y, then there is a

polynomial-time algorithm for X

c. If there is a polynomial-time reduction from X to Y, and X is NP-hard, then Y is NP-hard

d. If there is a polynomial-time reduction from X to Y, and Y is NP-hard, then X is NP-hard

e. None of these statements are true