Discrete math and rules of inference

Question

I recently did this rules of inference/logic question and the method I used was different from the textbook so I was wondering if my work was correct?

Answer 1

$(p\to q) \wedge (q\to b)$ implies $p\to b$, but not the other way around. Hence those two justifications are false as written. Fortunately, you only need them in one direction, the one that is true.