Transliteration:( Hudanw wa rahmatal lilmuhsineen )
3. It means the Holy Quran is a guide for the actions of the believers, while for the pious it is a guide to Paradise. From it we learn that worship is not obligatory upon the infidels. All the verses concerning acts of worship had been revealed for the believers.
The tafsir of Surah Luqman verse 3 by Ibn Kathir is unavailable here.
Please refer to Surah Luqman ayat 1 which provides the complete commentary from verse 1 through 7.
(31:3) a guidance and mercy for the doers of good,[2]
2. That is, these verses give guidance to the right way and have been sent down as a mercy from God. But the people who can profit by this mercy and guidance are only those who adopt a righteous attitude, who wish to become good, who crave for their own well being, whose quality is that they avoid the evil when they are warned of it, and follow the good when they are shown the ways to it. As for the wicked and mischievous people, they will neither profit by this guidance nor receive any share from this mercy.
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