Where are you supposed to write these short rez summaries on the actual LSAT? or are you just supposed to remember them in your hread- of so how are u supposed to remember

i dont understand a→b→c=a→c . shouldnt it be if c is true then a is true because c is at the end of the chain so to get to c a must have happened but how can a→c if we don't know if b happened

I dont really understand how we got Athena like where dod we just pull that out of and how is that in the slightest way related to proving the argument