How many different elements does A * B have if A has m elements and B has n elements?

Answer: mn

Step-by-step explanation:

A set refers to a well-defined collection of items.

For example : Set of natural numbers (N)

Set of rational numbers (Q).

A Cartesian product is a product of two different sets.

such as M = {1,2} and N={3,4}

Then M x N = { (1,3), (1,4), (2,3), (2,4) }

According to the properties of the Cartesian product of sets, if a set P has 'k' elements and an another set Q has 'r' elements, then the number of different elements in P x Q = kr

Similarly, if A has m elements and B has n elements, then A x B has 'mn' elements.

∴ The number of ifferent elements does A * B have if A has m elements and B has n elements = mn