A ∩ C = {2, 3, 5} ∩ (2, 5}
= {2,5}
B ∩ D = {1,2,3} ∩ {2,3,5}
= {2,3}
(A ∩ C) x (B ∩ D) = {2, 5} x {2, 3}
= {(2, 2) (2, 3) (5, 2) (5, 3)} … (1)
A x B = {2,3,5} x {1,2,3}
= {(2,1) (2, 2) (2, 3) (3, 1) (3, 2) (3, 3) (5, 1) (5, 2) (5, 3)}
C x D = {2, 5} x {2, 3, 5}
= {(2, 2) (2, 3) (2, 5) (5, 2) (5, 3) (5, 5)}
(A x B) ∩ (C x D) = {(2,2) (2, 3) (5, 2) (5, 3)} … (2)
From (1) and (2) we get
(A ∩ C) x (B ∩ D) = (A x B) ∩ (C x D)
