How to do this Cartesian Product of three sets?

B = {u, v}

C = {c, m}

Cartesian Product: B [X] C = set of all ordered pairs from B and C

D = B [X] C ={(u,c), (u,m), (v,c), (v,m)}

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A = {1, 2, 3}

D = {(u,c), (u,m), (v,c), (v,m)}

Cartesian Product: A [X] D = A [X] ( B [X] C ) = set of all ordered pairs from A and D

E = A [X] ( B [X] C ) = {(1,u,c), (1,u,m), (1,v,c), (1,v,m), (2,u,c), (2,u,m), (2,v,c), (2,v,m), (3,u,c), (3,u,m), (3,v,c), (3,v,m)}

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A = {1, 2, 3}

B = {u, v}

Cartesian Product: A [X] B = set of all ordered pairs from A and B

F = A [X] B = {(1,u), (1,v), (2,u), (2,v), (3,u), (3,v)}

C = {c, m}

Cartesian Product: F [X] C = ( A [X] B ) [X] C = set of all ordered pairs from F and C

G = ( A [X] B ) [X] C = {(1,u,c), (1,u,m), (1,v,c), (1,v,m), (2,u,c), (2,u,m), (2,v,c), (2,v,m), (3,u,c), (3,u,m), (3,v,c), (3,v,m)}

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comparing E & G

E = A [X] ( B [X] C ) = {(1,u,c), (1,u,m), (1,v,c), (1,v,m), (2,u,c), (2,u,m), (2,v,c), (2,v,m), (3,u,c), (3,u,m), (3,v,c), (3,v,m)}

G = ( A [X] B ) [X] C = {(1,u,c), (1,u,m), (1,v,c), (1,v,m), (2,u,c), (2,u,m), (2,v,c), (2,v,m), (3,u,c), (3,u,m), (3,v,c), (3,v,m)}

so

A [X] ( B [X] C ) = ( A [X] B ) [X] C = A [X] B [X] C = {(1,u,c), (1,u,m), (1,v,c), (1,v,m), (2,u,c), (2,u,m), (2,v,c), (2,v,m), (3,u,c), (3,u,m), (3,v,c), (3,v,m)}

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