S.O.S. Mathematics CyberBoard

Could someone please verify that my thinking is correct in both cases? Thank you!
1)~q => (~p => q)

~(~q) v (~p => q)
q v (~p=>q)
q v (~(~p) v q)
q v (p v q)
(q v q) v p
q v p

2) the same example ~q => (~p => q)
~(~q) v (~p => q)
q v (~p=>q)
(q v ~p) => (q v q)
~ (q v ~p) v q
(~q ^ p) v q
(~q v q) ^ (p v q)
T ^ (p v q)
p v q

Here's the WolframAlpha calculation.
Under minimal forms, you can see that p v q is one of the simplifications.

Thank you for the link. However, I would like to be sure that I am correctly applying the equivalences in all the steps. In other words if I am getting this result the right way.

Yes.

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Thank you!