Your logic is flawed. It is entirely possible for these three religions to be worshiping the same God while doing so in different ways, recognizing different prophets, believing in different texts, etc.
Not with one of them(Islam) encouraging the subjugation, killing or converting members of the other religions, and also the agnostics and athiests.
Try reading the Koran and Hadiths for further clarification and edification. - tom