Explanation:
The Cartesian product of two sets A and B, denoted by A x B, is the set of all ordered pairs (a, b), where a belongs to A and b belongs to B.
Here, A = {x: 0 < x < 4} and B = {y: 0 <= y <= 2}.
To find A x B, we pair each element of A with each element of B:
A x B = {(x, y) : x ∈ A, y ∈ B}
= {(x, y) : 0 < x < 4, 0 <= y <= 2}
We can represent A x B as a table of ordered pairs:
A x B
(1, 0)
(1, 1)
(1, 2)
(2, 0)
(2, 1)
(2, 2)
(3, 0)
(3, 1)
(3, 2)
Therefore, the Cartesian product of the sets A and B is:
A x B = {(1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (3, 2)}