Which of the following compounds is achiral?

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(A) compound is achiral if it possesses a plane of symmetry or a center of inversion.$A$: The $cis$-isomer of $2,6$-dimethyl-$1,4$-dioxane has a plane

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$2,6-$dimethyl$-1,4-$dioxane (cis-isomer)

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(A) compound is achiral if it possesses a plane of symmetry or a center of inversion.$A$: The $cis$-isomer of $2,6$-dimethyl-$1,4$-dioxane has a plane of symmetry passing through the oxygen atoms and bisecting the molecule,making it achiral.$B$: The $cis$-isomer of $2,5$-dimethylpiperazine is chiral as it lacks a plane of symmetry or center of inversion.$C$: $2,5$-dimethylcyclohexane-$1,4$-dione is chiral due to the absence of internal symmetry elements.$D$: $2$-methyl-$1,4$-dithiane is chiral because it has a stereocenter at the $C-2$ position and no symmetry elements.Therefore,the correct option is $A$.

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