Final answer:
The Cartesian product of sets A and B is the set of all ordered pairs (a, b) where a is in A and b is in B. The intersection of AxB is AxB itself. Therefore, n(AxB) = AxB = {(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)}.
Step-by-step explanation:
In set theory, the Cartesian product of two sets A and B, denoted by AxB, is the set of all ordered pairs (a, b) where a is in A and b is in B. Therefore, for A={2,4,6} and B={2,4,6}, the Cartesian product AxB is {(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)}.
Similarly, the Cartesian product BxA is {(2,2),(4,2),(6,2),(2,4),(4,4),(6,4),(2,6),(4,6),(6,6)}.
The intersection (n) of AxB is the set of elements that are common to both AxB and AxB, which in this case is AxB itself. Therefore, n(AxB) = AxB = {(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)}.
The intersection n(AxB) is the same as n(AxB) because both sets are equal.