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Have you looked on your lock screen? in the upper right corner?
I feel obligated to add to this. The upper right corner of the lock screen INITIALLY gives you choices between Sound On and Vibrate.
It is only after you get your phone into Mute some other way that your options are Sound On and Mute. And that second option will switch between Vibrate and Mute depending on the most recent way you have had your phone soundless.
(This particular fact has made me use vibrate mode extremely rarely, because I like having the option on my lock screen always be Mute, not Vibrate.)