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Let B = {0, 1}3 = {(0, 0, 0), . . . ,(1, 1, 1)} and...

Let B = {0, 1}3 = {(0, 0, 0), . . . ,(1, 1, 1)} and F = {Bi : i ∈ I} be the indexed family of sets where

I = {0, 1, 2, 3};

Bi = {(b1, b2, b3) ∈ B : b1 + b2 + b3 = i}.

Calculate the elements of F and show that F is a partition of B

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