A question on "finite substes of an infinite set".

I have a question from a book:

Let A be an infinite set, let S be a subset of P(A) satisfies:
1. Every B in S is a finite set.
2. U_{B \in S} B = A

show that A~S (A equipotent to S).
I have been thinking about this question for several days, hope one
could give me a hint.
I guess a simple trick will do, please do not use well-ordering
principal ...

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