If the relation R = {(x, x^3) : x is a prime number less than 10}, then the range of R is:
Model Answer & Options
Source: Extra Practice{8, 27, 125, 343}
{2, 3, 5, 7}
{1, 8, 27, 125, 343}
{8, 27, 64, 125}
Explanation
Prime numbers less than 10 are {2, 3, 5, 7}. The relation is defined as (x, x^3), so the range consists of the cubes of these primes: 2^3=8, 3^3=27, 5^3=125, and 7^3=343. Option B is the domain. Option C incorrectly includes 1 (1 is not prime). Option D includes 64 (4^3), but 4 is not a prime number.
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 a set A contains 3 elements and set B contains 4 elements, how many relations can be defined from set A to set B?