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Now that we have established that you CAN install an antenna system on your roof, the question remains "what to install" and do you want to install on your roof?
Neither antenna that you have suggested is suitable for your situation.
You are in a difficult location that is severely cut off by a mountain range, and while you are not that far from the Mt. Wilson, you have a badly obscured view of the transmitters. Your situation calls for a deep-fringe antenna system if you want to pick up the LA channels, and, even with such an antenna system, you may still have difficulty with some stations such as KNBC and KCET. Please let us know if you want to proceed, and I can detail what you'll need. here is a photo of the proposed antenna system:
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