A = {4,5,6}; B = {1,2} C = {0,1}
B ∩ C = {1,2} ∩ {0, 1}
= {1}
A x (B ∩ C) = {4,5,6} x {1}
= {(4, 1) (5, 1) (6, 1)} …. (1)
A x B = {4,5,6} x {1,2}
= {(4, 1) (4, 2) (5, 1) (5, 2) (6, 1) (6, 2)}
A x C = {4,5,6} x {0, 1}
= {(4,0) (4,1) (5,0) (5, 1) (6, 0) (6, 1)}
(A x B) ∩ (A x C) = {(4, 1) (5, 1) (6, 1)} … (2)
From (1) and (2) we get
A x (B ∩ C) = (A x B) ∩ (A x C)