Answer
A1 = {1, 2, 3}
A2 = {u, v}
A3 = {m,n}
a. A1 x (A2 x A3) = {1, 2, 3} x {(u, m), (u, n), (v, m), (v, n)}
= {(1, (u, m)), (1, (u, n)), (1, (v, m)), (1, (v, n)),
(2, (u, m)), (2, (u, n)), (2, (v, m)), (2, (v, n)),
(3, (u, m)), (3, (u, n)), (3, (v, m)), (3, (v, n))}
b. (A1 x A2) x A3 = {(1, u), (1, v), (2, u), (2, v), (3, u), (3, v)} x {m, n}
= {((1, u), m), ((1, u), n),
((1, v), m), ((1, v), n),
((2, u), m), ((2, u), n),
((2, v), m), ((2, v), n),
((3, u), m), ((3, u), n),
((3, u), m), ((3, u), n)}
c. A1 x A2 x A3 = {1, 2, 3} x {u, v} x {m, n}
= {(1, u, m), (1, u, n), (1, v, m), (1, v, n),
(2, u, m), (2, u, n), (2, v, m), (2, v, n),
(3, u, m), (3, u, n), (3, v, m), (3, v, n)}
Work Step by Step
A1 = {1, 2, 3}
A2 = {u, v}
A3 = {m,n}
a. A1 x (A2 x A3) = {1, 2, 3} x {(u, m), (u, n), (v, m), (v, n)}
= {(1, (u, m)), (1, (u, n)), (1, (v, m)), (1, (v, n)),
(2, (u, m)), (2, (u, n)), (2, (v, m)), (2, (v, n)),
(3, (u, m)), (3, (u, n)), (3, (v, m)), (3, (v, n))}
b. (A1 x A2) x A3 = {(1, u), (1, v), (2, u), (2, v), (3, u), (3, v)} x {m, n}
= {((1, u), m), ((1, u), n),
((1, v), m), ((1, v), n),
((2, u), m), ((2, u), n),
((2, v), m), ((2, v), n),
((3, u), m), ((3, u), n),
((3, u), m), ((3, u), n)}
c. A1 x A2 x A3 = {1, 2, 3} x {u, v} x {m, n}
= {(1, u, m), (1, u, n), (1, v, m), (1, v, n),
(2, u, m), (2, u, n), (2, v, m), (2, v, n),
(3, u, m), (3, u, n), (3, v, m), (3, v, n)}