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

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