If A = {x ϵ N : x ≤ 3} and {x ϵ W : x < 2}, find (A × B) and (B × A).

Given:

$A=\{x \in N: x \leq 3\}$

Here, N denotes the set of natural numbers.

$\therefore \mathrm{A}=\{1,2,3\}$

$[\because$ It is given that the value of $x$ is less than 3 and natural numbers which are less than 3 are 1 and 2]

and $B=\{x \in W: x<2\}$

Here, W denotes the set of whole numbers (non – negative integers).

$\therefore B=\{0,1\}$

$[\because$ It is given that $x<2$ and the whole numbers which are less than 2 are 0 and 1$]$

So, $A \times B=\{1,2,3\} \times\{0,1\}$

[By the definition of equality of ordered pairs .i.e. the corresponding first elements are equal and the second elements are also equal, but here the pair $(1,0)$ is not equal to the pair $(0,1)$ ]