Let A₁, A₂ be two countably infinite sets with A₁ A₂2 =/ 0. Let
A1 = A1 x {1}
A2 = A2 × {2}

Prove that Ã1 n Ã2 = 0 and card (Ã1 u Ã2) U = card (A1 U A2)