Question

If the set A has 3 elements and set B={3,4,5} then find the numbers of elements in$(A \times B)$.

Answer 1

Hint: First we’ll find the number of elements of set B then we’ll assume any three elements for set A. Now, we have set A and set B we can easily find the set $(A \times B)$. After finding the set $(A \times B)$. We’ll get the number of elements of $(A \times B)$.

Complete step by step solution: Given data: number of elements in set A=3
Set B={3,4,5}
Therefore, the number of elements in set B=3
Let the elements of set A are a, b, and, c
Therefore, set A={a,b,c}
Therefore, $(A \times B) = \{ (a,3),(a,4),(a,5),(b,3),(b,4),(b,5),(c,3),(c,4),(c,5)\} $

Therefore the number of elements in $(A \times B)$=9

Note: An alternative method for the solution of this question can be
number of elements in set A=3
Set B={3,4,5}
Therefore, the number of elements in set B=3
We know that if two sets let X and Y have m and n numbers of elements respectively then the number of elements in the sets $(X \times Y)$ or $(Y \times X)$ will be the product of the number of elements in the respective sets i.e. mn.
Therefore, the number of elements in the set $(A \times B) = 3 \times 3 = 9$