Given A = {1, 2, 3), B = (a, b) and C = (1, m, n). Find each of the following sets (i) AxBX C (ii) A x C. (iii) B XCx A.

(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))}