Identify the products of the given reactions.

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(C) In Reaction-$1$,the $-OTs$ group and the $-NMe_2$ group are in a cis-configuration. The nucleophilic attack by $CH_3COO^-$ occurs via an $S_N2$ me

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$A$ single product is obtained in both the reactions.

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(C) In Reaction-$1$,the $-OTs$ group and the $-NMe_2$ group are in a cis-configuration. The nucleophilic attack by $CH_3COO^-$ occurs via an $S_N2$ mechanism,resulting in inversion of configuration at the carbon atom bearing the $-OTs$ group. Since the starting material is chiral,the product is a single enantiomer.In Reaction-$2$,the $-OTs$ group and the $-NMe_2$ group are in a trans-configuration. The lone pair on the nitrogen atom of the $-NMe_2$ group participates in Neighboring Group Participation $(NGP)$,forming a cyclic aziridinium ion intermediate. This intermediate is then opened by the acetate nucleophile. Due to the symmetry and the nature of the $NGP$-assisted pathway,this reaction also leads to a specific stereochemical outcome,typically resulting in a single product (or a specific pair of enantiomers depending on the starting material's chirality). Given the options,the most accurate description is that a single product is obtained in both reactions due to the stereospecific nature of these pathways.

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