24:31وَقُل لِّلْمُؤْمِنَاتِ يَغْضُضْنَ مِنْ أَبْصَارِهِنَّ وَيَحْفَظْنَ فُرُوجَهُنَّ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا مَا ظَهَرَ مِنْهَا وَلْيَضْرِبْنَ بِخُمُرِهِنَّ عَلَىٰ جُيُوبِهِنَّ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا لِبُعُولَتِهِنَّ أَوْ آبَائِهِنَّ أَوْ آبَاءِ بُعُولَتِهِنَّ أَوْ أَبْنَائِهِنَّ أَوْ أَبْنَاءِ بُعُولَتِهِنَّ أَوْ إِخْوَانِهِنَّ أَوْ بَنِي إِخْوَانِهِنَّ أَوْ بَنِي أَخَوَاتِهِنَّ أَوْ نِسَائِهِنَّ أَوْ مَا مَلَكَتْ أَيْمَانُهُنَّ أَوِ التَّابِعِينَ غَيْرِ أُولِي الْإِرْبَةِ مِنَ الرِّجَالِ أَوِ الطِّفْلِ الَّذِينَ لَمْ يَظْهَرُوا عَلَىٰ عَوْرَاتِ النِّسَاءِ وَلَا يَضْرِبْنَ بِأَرْجُلِهِنَّ لِيُعْلَمَ مَا يُخْفِينَ مِن زِينَتِهِنَّ وَتُوبُوا إِلَى اللَّهِ جَمِيعًا أَيُّهَ الْمُؤْمِنُونَ لَعَلَّكُمْ تُفْلِحُونَ
And say to the believing women that they cast down their looks and guard their private parts and do not display their ornaments except what appears thereof, and let them wear their head-coverings over their bosoms, and not display their ornaments except to their husbands or their fathers, or the fathers of their husbands, or their sons, or the sons of their husbands, or their brothers, or their brothers' sons, or their sisters' sons, or their women, or those whom their right hands possess, or the male servants not having need (of women), or the children who have not attained knowledge of what is hidden of women; and let them not strike their feet so that what they hide of their ornaments may be known; and turn to Allah all of you, O believers! so that you may be successful.
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Salam All, As per this Ayah the Muslim women have to cover their Head with Khimar and cover their Bossom with a cloth. Bro Joseph Islam has also discussed in his article. But some Muslim Schlars like Allama Ghamidi don't agree. As per Quran covering Hair & bossom is necessary.