Thanks Dave,
The only place I could find any Adobe Pluginson my computer was where etresoft (above) said they would be. Etrosoft said: "Go to ~/Library/Internet Plug-Ins (Finder > Go > option key > Library) and /Library/Internet Plug-ins (Finder > Go > Go to Folder) and remove anything that says PDF or Adobe." Sure enogh, by following that path I found two plugins called "AdobePDFViewer and pluginNPAPI.plugin. I removed them both, placing them in a folder on a tumb drive with instructions of how and where to put them back if need be. Anyhow, removing them certainly solved the problem, and now I can open PDF's in Safari again.
I am using a 13" macbook air that I purchased just a few months ago from apple. That being said I know I did not download any PDF plugins directly from adobe. When I first purchased my macbook air I had no problems opening up PDF's on the internet using Safari. However, a few weeks ago I downloaded a trial version of a software called Circus Ponies Notebook that I was thinking about using to help me with my research. It's all a little blurry now, as two weeks have gone by, but I am pretty sure that the problems I was having started a few weeks ago as well. But again, I’m not certain. That being said, Circus Ponies does open up PDF’s and also has features for importing PDF’s into its database. So maybe it uses the Adobe PDF plugin as its importing/reading engine, and maybe the Adobe plugin was part and parcel to the download. I imagine this could be the case with any app that can open/Import/read PDF’s, and there are quite a few of them out there.
Anyhow, my problem was completely solved by following the advice from etresoft, as seen above. So thanks to y'all for the giving of your valuable time to contribute to the apple support forums. I have been part of the mac family for many years now and have mostly found the folks on the support forums to be gracious and helpful. My wife uses a PC, and as the techie in my family (relatively speaking), I have not experienced anywhere near this same level of camaraderie within the Microsoft community.