(i) AxBX C:
The Cartesian product of A and B is the set of all possible ordered pairs that can be formed by taking one element from A and one element from B.
So, AxB is {(1,a), (1,b), (2,a), (2,b), (3,a), (3,b)}.
Then, taking the Cartesian product of AxB with C gives us the set of all possible ordered triples formed by taking one element from AxB and one element from C:
AxBXC = {((1,a,1), (1,a,m), (1,a,n), (1,b,1), (1,b,m), (1,b,n), (2,a,1), (2,a,m), (2,a,n), (2,b,1), (2,b,m), (2,b,n), (3,a,1), (3,a,m), (3,a,n), (3,b,1), (3,b,m), (3,b,n))}
(ii) A x C:
The Cartesian product of A and C is the set of all possible ordered pairs formed by taking one element from A and one element from C.
So, AxC is {(1,1), (1,m), (1,n), (2,1), (2,m), (2,n), (3,1), (3,m), (3,n)}.
(iii) B XCx A:
The Cartesian product of B and C is the set of all possible ordered pairs formed by taking one element from B and one element from C.
So, BxC is {(a,1), (a,m), (a,n), (b,1), (b,m), (b,n)}.
Taking the Cartesian product of BxC with A gives us the set of all possible ordered triples formed by taking one element from BxC and one element from A:
BXCxA = {((a,1,1), (a,1,2), (a,1,3), (a,m,1), (a,m,2), (a,m,3), (a,n,1), (a,n,2), (a,n,3), (b,1,1), (b,1,2), (b,1,3), (b,m,1), (b,m,2), (b,m,3), (b,n,1), (b,n,2), (b,n,3))}