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(A) Let $C$ denote Compulsory and $O$ denote Optional.$1$. $F$'s compulsory subject is Mathematics. $F$ also has Physics as a subject,so Physics is $F

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History

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(A) Let $C$ denote Compulsory and $O$ denote Optional.$1$. $F$'s compulsory subject is Mathematics. $F$ also has Physics as a subject,so Physics is $F$'s optional subject.$2$. $E$ and $F$ have Physics as a subject. Since $F$ has Physics as optional,$E$ must have Physics as a compulsory subject.$3$. $C$ and $E$ have Mathematics as an optional subject.$4$. $A$ and $D$ have History and English as their subjects. $D$'s optional is History,so $D$'s compulsory is English. $A$'s subjects are the reverse of $D$'s,so $A$'s compulsory is History and optional is English.$5$. History is a compulsory subject for three teachers. We know $A$ has it as compulsory. Since $D$ is the only female teacher (English compulsory),and $B$ and $C$ are the remaining candidates,History must be the compulsory subject for $B$ and $C$.$6$. Chemistry is an optional subject for only one teacher. Since all other slots are filled,$B$ must have Chemistry as an optional subject.Thus,$C$'s compulsory subject is History.

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