Final answer:
To find A x B, we combine every element in A with every element in B. The set of ordered pairs in the relations 'is less than', 'is greater than', and 'is equal to' from A to B are determined based on the comparison of the elements.
Step-by-step explanation:
To find the cartesian product of set A and set B, we need to combine every element in set A with every element in set B. So, the cartesian product of A and B, denoted as A x B, is {(2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (4, 3)}.
The set of ordered pairs in the relation 'is less than' from A to B consists of all pairs where the first element is less than the second element. So, the set of ordered pairs is {(2, 3), (2, 2), (3, 3), (3, 2), (4, 3), (4, 2)}.
The set of ordered pairs in the relation 'is greater than' from A to B consists of all pairs where the first element is greater than the second element. So, the set of ordered pairs is {} (empty set).
The set of ordered pairs in the relation 'is equal to' from A to B consists of all pairs where the first element is equal to the second element. So, the set of ordered pairs is {(2, 2), (3, 3)}.