A = {1,2,3}, B = {2,3,5}, C = {3,4} D = {1,3,5}
A ∩ C = {1,2,3} ∩ {3,4}
= {3}
B ∩ D = {2,3, 5} ∩ {1,3,5}
= {3,5}
(A ∩ C) x (B ∩ D) = {3} x {3,5}
= {(3, 3)(3, 5)} … (1)
A x B = {1,2,3} × {2,3,5}
= {(1,2) (1,3) (1,5) (2, 2) (2, 3) (2, 5) (3, 2) (3, 3) (3, 5)}
C x D = {3,4} × {1,3,5}
= {(3,1) (3, 3) (3, 5) (4,1) (4, 3) (4, 5)}
(A x B) ∩ (C x D) = {(3, 3) (3, 5)} … (2)
From (1) and (2) we get
(A ∩ C) x (B ∩ D) = (A x B) ∩ (C x D)
This is true.
