[Mention, O Muhammad], when the wife of 'Imran said, "My Lord, indeed I have pledged to You what is in my womb, consecrated [for Your service], so accept this from me. Indeed, You are the Hearing, the Knowing."
But when she delivered her, she said, "My Lord, I have delivered a female." And Allah was most knowing of what she delivered, "And the male is not like the female. And I have named her Mary, and I seek refuge for her in You and [for] her descendants from Satan, the expelled [from the mercy of Allah ]."
So her Lord accepted her with good acceptance and caused her to grow in a good manner and put her in the care of Zechariah. Every time Zechariah entered upon her in the prayer chamber, he found with her provision. He said, "O Mary, from where is this [coming] to you?" She said, "It is from Allah . Indeed, Allah provides for whom He wills without account." (Quran 3:34-37)
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By reading the verses above one should be able to deduce wife of Imran named her daughter Mary, and Mary was under the care of Zecharia a.s.
As it clearly states that Mary is living in the time Zecharia a.s
So when one reaches the verse 19:28, an issue of mistaken identity doesn't appear at all . The only thing that will cause one to ponder is why the people address her sister of Aaron? Were they calling her with a title sister of prophet Aaron or prophet Moses? Or sister of a person named Aaron?
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Some fact, wife of Imran named her daughter Mary based on name of past pious people.