ANSWER:

It is not a must to fast the Friday as well in this situation because you can fast the day of Arafah alone even if it falls on a Friday or a Saturday, this is an exception just like Ashoora. 

If the day of arafah happens to be on a Saturday do we have to fast the Friday as well? I have heard that we are not allowed to fast Saturdays or Sundays by themselves as they are days of the Jews and Christians.

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