Let \( A \) and \( B \) be two sets each with a finite number of elements. Assume that there is ...

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Let \( A \) and \( B \) be two sets each with a finite number of elements. Assume that there is an injective mapping from \( A \) to \( B \) and th at there is an injective mapping from \( B \) to \( A \). Prove that there is a bijective mapping from \( A \) to \( B \).
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