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(D) Let '$C$' denote a compulsory subject and '$O$' denote an optional subject.						Subject			$A$			$B$			$C$			$D$			$E$			$F$							History			$C$

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$A, B, C$

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(D) Let '$C$' denote a compulsory subject and '$O$' denote an optional subject.						Subject			$A$			$B$			$C$			$D$			$E$			$F$							History			$C$			$C$			$C$			$O$			-			-							Physics			-			-			-			-			$C$			$O$							Mathematics			-			-			$O$			-			$O$			$C$							English			$O$			-			-			$C$			-			-							Chemistry			-			$O$			-			-			-			-			$1$. $F$'s compulsory subject is Mathematics. $F$ has Physics as one of the subjects,so Physics is an optional subject for $F$.$2$. $E$ has Physics as one of the subjects. Since $F$'s optional is Physics,$E$ must have Physics as a compulsory subject.$3$. $A$ and $D$ have History and English. $D$'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.$4$. Chemistry is an optional subject for only one person,which must be $B$.$5$. History is a compulsory subject for three teachers. Since $A$ has it as compulsory,and $D$ has it as optional,the other two must be $B$ and $C$.$6$. Thus,$A, B,$ and $C$ have History as their compulsory subject.

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