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This surah includes seeking refuge from the evil that causes all sins and acts of disobedience: the evil within a person that gives rise to punishment in this world and the Hereafter.
Surah al-Falaq includes seeking refuge from the evil of others wronging a person through sorcery and envy. This is an external evil.
Surah al-Nās includes seeking refuge from the evil that causes a servant to wrong himself. This is an internal evil.
The first evil falls outside the scope of his moral responsibility, and he is not required to desist from it, since it is not his own doing.
The second evil, addressed in Surah al-Nās, falls within the scope of moral responsibility and is subject to prohibition. This is the evil of personal faults, whereas the first is the evil of afflictions. All evil comes down to faults and afflictions; there is no third category.
Thus, Surah al-Falaq includes seeking refuge from the evil of afflictions, while Surah al-Nās includes seeking refuge from the evil of faults, all of which have their root in whispering.
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With this understood, waswās (whispering) follows the pattern faʿlāl and is derived from waswasa (to whisper).
The basic meaning of whispering is a subtle movement or sound that goes unnoticed, so that one does not guard against it.
Whispering, then, is the covert suggestion of something to the soul, either through a faint voice heard only by the person to whom it is directed, or without any sound, as Satan whispers to a servant.