Let A = {x ∈ w/3 < x < 7}, B = {x ∈ N/0 < x < 3}, C = {x ∈ w/x <

1.	Let A = {x ∈ w/3 < x < 7}, B = {x ∈ N/0 < x < 3}, C = {x ∈ w/x < 2} verify A x (B ∩ C) = (A x B) ∩ (A x C)
Answer» 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)

Let A = {x ∈ w/3 < x < 7}, B = {x ∈ N/0 < x < 3}, C = {x ∈ w/x < 2} verify A x (B ∩ C) = (A x B) ∩ (A x C)

Answer»

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)