Suppose that Φ1 and Φ2 are decision problems and that there is apolynomial time reduction from Φ1 to Φ2. For each of the followingquestions, say whether the answer is true or false, and give abrief explanation of your answer:

(1) If Φ1 is in P, must Φ2 be in P?

(2) If Φ2 is in P, must Φ1 be in P?

(3) If there is a polynomial time reduction from Φ2 to Φ1, Φ1and Φ2 are both NP-complete.

## Expert Answer

Answer to Suppose that Φ1 and Φ2 are decision problems and that there is a polynomial time reduction from Φ1 to Φ2. For each o…