The right sign for "cover" depends on what you are covering.
If you are at a restaurant and want to pay for your ASL instructor's
meal as in "I'll cover this" then the sign you want to use is "PAY."
If you are covering a jar then your non-dominant hand is going to
need to be a "C" handshape (to represent the jar) and your dominant
hand can be a flat hand. If you are trying to tell someone to
"cover their mouth when they cough" you would sign HAPPEN YOU COUGH
and then mime for them the act of coughing into the crook of their
elbow. If you are talking about covering a bowl of food, you might
want to mime the act of stretching and smoothing plastic wrap onto a
bowl. If you are discussing covering up a dead body after last
night's zombie attack then you might want to mime pulling a blanket
over the body.
General sign for COVER:
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