I have a question? is someone buys a gig and it has not been delivered but i show them a preview of the logo? can they cancel the whole thing and take the logo…?
No, they shouldn’t be doing that.
I recommend sending the buyer thumbnail samples, or applying a watermark to all sample images. This reminds the buyer that you are providing them with a sample to get their opinion, and that the final delivered image will be useable at the professional high quality level they likely hired you for.
If they cancel and get the refund, they have no legal right to use the logo you created. If they use it anyway, you can sue them for it (I don’t know what would be the procedure for it, but I do know that, until they pay you for the logo, you keep all the rights).