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(D) Let $C$ denote Compulsory and $O$ denote Optional.						Subject			$A$			$B$			$C$			$D$			$E$			$F$							History			$C$			$C$			$C$			$O$			-			-

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$D$

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(D) Let $C$ denote Compulsory and $O$ denote Optional.						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. Since $F$ also teaches Physics,Physics must be $F$'s optional subject.$2$. $E$ has Physics as one of his subjects. Since Mathematics is $E$'s optional subject,Physics must be $E$'s compulsory subject.$3$. $A$ and $D$ have History and English. $D$'s optional is History,so $D$'s compulsory is English.$4$. $A$'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 people. We know $A$ has it as compulsory. Since $B$ and $C$ are the only ones left for the third compulsory slot,and Chemistry is the optional subject of only one person $(B)$,we deduce the table above.$6$. The problem states the only female teacher has English as her compulsory subject. Looking at the table,$D$ has English as her compulsory subject.Therefore,$D$ is the female member.

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