Should she obey her father and not fast?

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He wants to continue fasting so that he can give up smoking
Ruling on making up six days of Shawwaal in Dhu’l-Qa‘dah

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Related Answers:
Combining making up a missed Ramadan fast with the fast of ‘Ashoora’ or ‘Arafah
How is the fast of Dawood (peace be upon him) observed, and how can that be reconciled with the prohibition on fasting on Fridays?
Will the person who intends to fast ‘Ashoora during the day be rewarded for his fasting?
He wants to continue fasting so that he can give up smoking
Ruling on making up six days of Shawwaal in Dhu’l-Qa‘dah

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