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(D) For a substrate to give the same product in both $S_{N^1}$ and $S_{N^2}$ reactions,the carbocation formed in $S_{N^1}$ must not undergo rearrangem

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$(III) \ \& \ (IV)$

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(D) For a substrate to give the same product in both $S_{N^1}$ and $S_{N^2}$ reactions,the carbocation formed in $S_{N^1}$ must not undergo rearrangement,and the $S_{N^2}$ reaction must occur at the same carbon without stereochemical complexity that leads to different products.$(I)$ $CH_3-CH(CH_3)-CH_2-CH(Br)-CH_3$ is a secondary halide that can undergo rearrangement to a more stable carbocation.$(II)$ $	ext{2-methylcyclohexyl chloride}$ is a secondary halide where the carbocation can rearrange.$(III)$ $	ext{Chlorocyclohexane}$ is a secondary halide. The carbocation formed is a cyclohexyl cation which does not rearrange. $S_{N^2}$ occurs at the same carbon.$(IV)$ $CH_3-CH(Br)-CH_2-CH_3$ is a secondary halide $(2	ext{-bromobutane})$. The carbocation formed is a secondary carbocation which does not rearrange. $S_{N^2}$ occurs at the same carbon.Thus,$(III)$ and $(IV)$ give the same product in both mechanisms.

Among the given halides,which one will give the same product in both $S_{N^1}$ and $S_{N^2}$ reactions?
$(I) \ CH_3-CH(CH_3)-CH_2-CH(Br)-CH_3$
$(II) \ \text{2-methylcyclohexyl chloride}$
$(III) \ \text{Chlorocyclohexane}$
$(IV) \ CH_3-CH(Br)-CH_2-CH_3$

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Among the given halides,which one will give the same product in both $S_{N^1}$ and $S_{N^2}$ reactions?$(I) \ CH_3-CH(CH_3)-CH_2-CH(Br)-CH_3$$(II) \ \text{2-methylcyclohexyl chloride}$$(III) \ \text{Chlorocyclohexane}$$(IV) \ CH_3-CH(Br)-CH_2-CH_3$