I'm having a hard time reducing expressions involving "implies" operators. I did some reading about the actual meaning of the "implies" operator and browse for other Q&A on this website; however, I don't know how to interpret expressions. For example, I have:
$(C1) A \implies B$ $(C2) C \implies B$
And I as a definition given in the context I know that: $ C \implies A$
Now, I'm being asked to prove or disprove: $ a) C1 \implies C2$ and $ b) C2 \implies C1$
Here is where my problem/question, for a) is it valid to do the following?
$ (A \implies B) \implies (C \implies B)$
and then (somehow):
$ A \implies C$
Based on my definition given a above, I'm thinking I could "disprove" a) and "prove" b) but I'm not sure if logic has any foundation.
Any help would be appreciated