write the set of all integers whose cube is an even integer

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{cube} \mathrm{of} \mathrm{even} \mathrm{integers} \mathrm{is} \mathrm{even}. \\ \mathrm{Hence} \mathrm{writing} \mathrm{in} \mathrm{set} \mathrm{builder} \mathrm{form} \mathrm{we} \mathrm{get} \mathrm{required} \mathrm{set} \mathrm{as} \\ \mathrm{S}=\left\{2\mathrm{x}: \mathrm{x}\in \mathrm{Q}, \mathrm{Q} \mathrm{represents} \mathrm{set} \mathrm{of} \mathrm{all} \mathrm{inetegrs}\right\} \end{gathered}$$

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