If set A has 4 elements and set B has 5 elements, then find the total number of elements in the Cartesian product A×B:

Correct option is C

The Cartesian product A×B involves pairing every element of set A with every element of set B.
· Set A has 4 elements.
· Set B has 5 elements.
The total number of elements in A×B is calculated as:
Number of elements in A×B=∣A∣×∣B∣ = 4×5 = 20
Thus, the total number of elements in A×B is 20.
Important Key Points:
1. Definition of Cartesian Product: The Cartesian product A×B is the set of all ordered pairs (a,b), where a∈A and b∈B.
2. Formula: The number of elements in A×B is the product of the number of elements in A and B: ∣A×B∣=∣A∣×∣B∣
3. Practical Applications: Cartesian products are widely used in mathematics, databases (relational algebra), and programming.
Knowledge Booster:
· Example of Cartesian Product: If A = {1, 2} and B = {x, y, z}, then:
A×B = {(1, x), (1, y), (1, z), (2, x), (2, y), (2, z)}
Total elements = 2×3 = 6.
· Properties of Cartesian Products:
· A×B≠B×A(order matters).
· If either A or B is empty, A×B=∅.