Question

The relation R = {(x, $x^{\frac{1}{3}}$):x is a natural number less than 1000}. Find range such that all the elements of the range are integers.

• A. Range = {1, 2, 3, 4, 5, 6, 7, 8, 9}
• B. Range = {1, 8, 27, 64, 125, 216, 343, 512, 729}
• C. Range = {1, 4, 9, 16, 25, 36, 49, 64, 81}
• D. Range = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Answer 1

The correct option is A

Range = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Relation R ={(x, $x^{\frac{1}{3}}$ ) : x is a natural number less than 1000; $x^{\frac{1}{3}}$ is an integer}

Relation R = {(1, 1), (8, 2), (27, 3), (64, 4), (125, 5), (216, 6), (343, 7), (512, 8), (729, 9)}

Domain = {1, 8, 27, 64, 125, 216, 343, 512, 729}

Set of first components of all the ordered pairs which belong to R

Range = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Set of second components of all the ordered pairs which belong to R.