If the set A has 3 elements and the set B = {3, 4, 5}, then the number of elements in (A × B) is:
Model Answer & Options
Source: Extra Practice3
6
9
27
Explanation
The number of elements in the Cartesian product A × B is given by n(A × B) = n(A) × n(B). Here, n(A) = 3 and B = {3, 4, 5} so n(B) = 3. Therefore, n(A × B) = 3 × 3 = 9. Option B incorrectly adds the counts. Option D treats it as 3^3.
Take Topic Quiz
Test your understanding of this topic with instant AI feedback.
Related Questions
- →
Let A = {1, 2, 3} and B = {x, y}. What is the total number of non-empty relations that can be defined from set A to set B?
- →
Let R be a relation on the set of natural numbers N defined by R = {(x, y) : x + 2y = 10; x, y ∈ N}. Which of the following represents the Range of R?
- →
If the Cartesian product A × B has 9 elements and contains the ordered pairs (-1, 0) and (0, 1), which of the following is set A?
- →
Let R be a relation on the set of natural numbers N defined by R = {(x, y) : x + 2y = 8}. The range of R is:
- →
If the relation R = {(x, x^3) : x is a prime number less than 10}, then the range of R is: