Thanks to everyone who has replied. This issue has nothing to do with notifications (email or alarm aka notification). It also has nothing to do with Google. When you set up a new event, or edit an existing event, you should see two options available at the bottom left of the screen. One is "I'm Busy", and the other is "I'm Available". Depending how how you have set up your preferences one or the other will already be selected. You can change your selection at an time.
This is my first Samsung phone. Before this I had several Motorola phones. Whenever I had a caledar event where BUSY was selected, my phone was silent for the entire length of the event. It wouldn't ring if a call was coming in, and all alarms would be silenced. In other words, if I was in a meeting, and that meeting was on my calendar and marked that "I'm Busy", my phone was silent! I didn't have to power it off to keep it from interupting. When that meeting was done all sounds resumed. Notices still showed up to let me know if I missed a call, or someone left a message, or someone sent a text, or I received email, etc. The only difference between BUSY and AVAILABLE was sound.
I have a hard time believing that Samsung has decided to deliberately ignore the Google calendar BUSY command! That is what all of the Samsung store reps have told me. It must be awfully difficult for Samsung to have a company meeting with all of those phones interrupting them. Or do they all use Motorola phones?