Question

Write the set \[A = \{ x:{x^3} - x,x \in R\} \] in the roaster form.

Answer 1

Hint: Here in the given question of set theory we need to solve the given term in roaster form, we know that roaster form expression contains the elements of the set separated by putting commas. In order to solve the above question we need to get the element by assuming any real number and then we can express the other elements of the set.

Complete step by step answer:
 Here in the given set of questions we need to solve by expanding the term given by putting the assumed value from any real number and accordingly we can get the solution for the question. As one of the term is obtained then accordingly we can write for the other terms also and can express in the roaster form, on solving we get:
Assuming the value of real number as one, we get:
\[
   \Rightarrow A = \{ x:{x^3} - x,x \in R\} \\
   \Rightarrow x = 0 \\
   \Rightarrow A = {0^3} - 0 = 0 \\
   \Rightarrow x = 1 \\
   \Rightarrow A = {1^3} - 1 = 0 \\
   \Rightarrow x = 2 \\
   \Rightarrow A = {2^3} - 2 = 6 \\
   \Rightarrow x = 3 \\
   \Rightarrow A = {3^3} - 3 = 24 \\
   \Rightarrow x = 4 \\
   \Rightarrow A = {4^3} - 4 = 60 \\
 \]
Now representing in roaster form we get:
\[ \Rightarrow A = \{ 0,6,24,60...\} \]
Here we get the following expression in roaster form.

Note: Here the given question needs to express the set term in roaster form, in order to get this solved we need to know about the roaster form, here roaster form says that the term should be differentiated by commas and written accordingly.