Math Problem Statement
If ,n (A)=3, n(B)= 4 then n(A×A×B)=
Solution
The problem asks to find , where and .
To solve this, we need to understand the Cartesian product. If represents the Cartesian product of the sets , , and , then the number of elements in the Cartesian product is the product of the number of elements in each set.
The formula for the number of elements in a Cartesian product of sets is:
Substituting the given values:
Thus, .
Would you like more details or have any questions?
Here are 5 related questions to explore further:
- What is the general formula for the Cartesian product of multiple sets?
- How does the Cartesian product differ from the union and intersection of sets?
- How would the result change if and ?
- Can Cartesian products be performed on infinite sets? How would behave in that case?
- What are some practical applications of the Cartesian product in real-life scenarios?
Tip: Always confirm the interpretation of the symbols in a problem, especially in set theory where notations can vary across contexts.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Set Theory
Cartesian Product
Formulas
n(A × A × B) = n(A) × n(A) × n(B)
Theorems
Cartesian Product Formula
Suitable Grade Level
Grades 6-8