Question

Write the following in set-builder form:-i) Set of all +ve integers whose cube is odd ii) Set of all real numbers which cannot be written as the quotient of two integers

Answer 1

$$\begin{gathered} \left(1\right)setofall+veintegerswhosecubeisodd. \\ Weknowthat,cubeofevennumberiseven.andcubeofoddnumberisodd. \\ So,insetbuilderform, \\ \left\{x:x=2m+1;m\ge 0andmisaninteger\right\} \\ \left(2\right)Setofallrealnumberswhichcannotbewriitenasthequotientoftwointegers \\ iscalledrealandirrationalnumber. \\ So,insetbuilderform, \\ \left\{x:xisrealandirrational\right\} \end{gathered}$$