True or False, with a proof or counterexample.

a) If bn ≠ 0 and an/bn →1, then an-bn → 0

b) If bn ≠ 0, bn is bounded and an/bn → 1 then an-bn → 0

At the moment I cannot even see which is false so I am struggling with this question. I think the proof will require use of the quotient combination rule and the sum combination rule but I cannot see where to start! Any help would be appreciated!