A X (B U C) = (A X B) U (A X C)
let A= {1,3} B={1,2} and C={2,3}
L.H.S-
Ax(BUC)
= {1,3} x ({1,2} U {2,3})
= {1,3} x { 1,2,3 }
= { (1,1) (1,2) (1,3) (3,1) (3,2) (3,3) }
R.H.S-
(A x B) U (A x C)
= ( {1,3} x {1,2} ) U ( {1,3} x {2,3} )
= { (1,1) (1,2) (3,1) (3,2) } U { (1,2) (1,3) (3,2) (3,3) }
= { (1,1) (1,2) (1,3) (3,1) (3,2) (3,3) }
therefore, LHS = RHS