The problem is there is no "delete" opportunity. Selecting a photo in photo library, having selected "edit", only gives the options to "share" or "add to". There appears to be no way to delete the photo. Only in "camera roll" is there a delete option.
That is correct. Photos in the Camera Roll are the only ones that can be deleted on the phone. Photos that are in the Photo Library are ones that are synced from the computer to the phone and have to be deleted in the same fashion. Connect the phone to the computer, open iTunes, go to the Photo tab and unselect the photo folder, or delete the unwanted pictures from the group of pictures and sync the phone again. This will remove them.
This is what finally worked for me after digesting the wonderful responses:
1. Launched iPhoto
2. Launched iTunes
3. In iPhoto I found the photos I wanted to delete and delted them.
4. In iTunes under the photo tab, I selected "synch to iPhoto"
5. Selected the Albums, Events, etc. I wanted to synch.
6. Synched my iPhone (and later my iPad).
7. When the synch was over, the photos I did not want were gone!
Thanks everyone. I hope this helps someone else.