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Lit., "has made [or "provided"] for you mates out of yourselves". The term zawj denotes not only "a pair" or "a couple" but also - as in this instance - "one of a pair" or "a mate" of the opposite sex; hence, with reference to human beings, the plural azwaj signifies both "husbands" and "wives".
Lit., "they", i.e., those who deny the truth of God's existence and/or oneness.
Ḥafadah means grandchildren, but can also mean children-in-law.
Of your nature: or of yourselves. Cf. iv. 1 and n. 504, Self, or Personality, or Soul, all imply a bundle of attributes, capacities, predilections, and dispositions, which we may sum up in the word Nafs, or nature. Woman was made to be (1) a mate or companion for man; (2) except for sex, of the same nature as man, and therefore, with the same moral and religious rights and duties; and (3) she is not to be considered a source of all evil or sin, as the Christian monks characterised her but rather as a blessing, one of the favours (Ni'mat) of Allah.
Hafadat: collective plural, grandchildren, and descendants. The root hafada also implies obedient service and ministration. Just as the sons (first mentioned) should be a source of strength, so daughters and grandchildren should serve and contribute to the happiness of fathers and grandparents, and are to be looked upon as further blessings.