Question

Write the relation R={$(x, {x^3})$ :x is the prime number less than 10} in roster form.

Answer 1

Hint: First we will find all the prime numbers that are less than 10, finding those prime numbers we’ll find the elements of R with-respect-to those prime numbers.
Combining all those elements written as a single set we’ll get the required roster form of R.

Complete step by step solution: Given data: R={$(x,{x^3})$ :x is the prime number less than 10}
We know that when a set is written in the form of all its elements then this form of the set is known as the roster form.
A prime number is that number divisible by 1 and itself only or the factors of that number are only 1 and the number itself.
Therefore, all the prime numbers less than 10 are 2, 3, 5 and, 7
Therefore the relation \[R = \left\{ {(2,{2^3}),(3,{3^3}),(5,{5^3}),(7,{7^3})} \right\}\]

\[\therefore R = \left\{ {(2,8),(3,27),(5,125),(7,343)} \right\}\] which is also the roster form of R.

Note: Here we have taken prime numbers like 2, 3, 5 and, 7, but some students may count 1 as well as it satisfies both the condition according to the definition of a prime number but there is also a definition of prime number that it has only two factors which are not satisfied by 1, hence not included under the category of prime numbers.