The first two premises do not form a valid chain, since affirming A or C produces a conclusion, B, which cannot be used as the minor premise in a valid argument with the other claim. Therefore, only premises 2 and 3 form the chain. Now try again to draw a valid conclusion. Only quiet places are restful. The places where I like to study are restful.
All libraries are quiet places.
All restful places are quiet places. My study places are restful places. All A are B. 2. All C are B 3. The first two premises do not form a valid chain, since affirming A or C produces a conclusion, B, which cannot be used as the minor premise in a valid argument with the other claim.