Question

If A=& B={2,4,6} find the relations in

(i)AxB
(ii) BxA
(iii) n(AXB)
(iv) n(AXB)​

Answer 1

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.